Ain Shams University Physics Laboratory Manual PDF

# Laboratory Manual of Physics I ## Women's College for Arts, Science and Education Ain Shams University Physics Department -1- ## Student's Name: ## Program: ## Lab Day: ## Lab Time: -2- ## Contents | Code | Experiment | Page | |---|---|---| | **PROPERTIES OF MATTER** | | | | 1 | Introd...

# Laboratory Manual of Physics I ## Women's College for Arts, Science and Education Ain Shams University Physics Department -1- ## Student's Name: ## Program: ## Lab Day: ## Lab Time: -2- ## Contents | Code | Experiment | Page | |---|---|---| | **PROPERTIES OF MATTER** | | | | 1 | Introduction to Graphs | 4 | | 2 | Measurement of Fundamental Quantities | 6 | | 3 | Free Fall | 15 | | 4 | Simple Pendulum | 19 | | | Verification of Boyle's Law of Gases (computer) | 25 | | **HEAT** | | | | | Introduction to Heat | 28 | | 5 | Latent Heat of Fusion of Ice | 30 | | 6 | Gay Lussac's Law | 34 | - 3- ## Introduction to Graphs Wherever possible, the results of an experiment should be presented in graphical form. Not only does a graph provide the best means of averaging a set of observations but also the dependence between the quantities is clearly shown. In plotting the results, the dependent variable should be plotted as ordinates on the y-axis and the independent variable as abscissa on the x-axis. The scale used should be a convenient one for arithmetical work and should be sufficiently extensive for the graph to occupy a wide sweep of space available. Each point on the graph is an actual observation, and should be made to stand out by surrounding it with a small circle. The departure of the point from the final curve is a measure of the experimental error in that observations should be taken over as wide range as possible, and the graph confined to the limits of the observations. In taking gradients, the full range of the graph (if a straight line) should be used, and for extrapolated values, the graph is continued as a broken line and the result followed by the statement "extrapolated value indicating that it is outside the limits of actual observations". - 4- ## The straight line equation: Most of the relations which we will be dealing with are linear relation, the general formula of the straight line in standard notation is: $$y = mx$$ - x: the independent variable and is plotted on the x-axis. - y: the dependent variable and is plotted on the y-axis. - m: the slope of the line. ### Example: The image shows a graph with a line and two points with coordinates (X1,Y1) and (X2,Y2). The slope of the line is defined as: $$Slope = \frac{Y_2 - Y_1}{X_2 - X_1}$$ From the figure, the slope can be calculated as: $$Slope = \frac{\Delta y}{\Delta x}$$ - 5- # Experiment No. (1) ## Measurement of Fundamental Quantities Our understanding of the physical universe ultimately depends on measurements of distance, length and time. Such measurements are always subject to some uncertainty. In this laboratory exercise, you will acquaint yourself with some fundamental measurement techniques. You will also be introduced to some elementary methods for treating the errors associated with these measurements. ### Mass Mass is a fundamental unit of measurement. We know it is "stuff" that takes up space and has a volume. A unit of mass is established by taking an arbitrary amount of a material and defining it as 1 unit. The unit of mass in the metric system is 1 kilogram. In the English system, the effect of gravity on a unit of mass is measured, such that 1 pound is the unit of weight in that system. Mass is usually denoted by the symbol _m_. ### Determination of a mass of a body by means of the balance - Make sure that the pans of the balance are clean and dry. - Level the balance case by means of the leveling screws. - Turn the handle of the balance so as to release the beam, and see that the beam rests without constraint on the knife-edges. - Observe the mean positions of the pointer on the scale as the beam swings from side to side. - Use the screw to stop the swinging of the balance when the pointer is near the mean position. - Place the unknown mass on the left hand pan, and place in the middle of the right-hand pan weights estimated to be enough to counter balance the load on the left. - Count the weights as they lie on the scale-pan and record the result. - Return the weights which are used in its exact position in the box. - You must determine the weight very accurate of milligram. - Do not put any hot body in the pan. - Do not put or pull the weight from the balance pan if the handle of the balance is pulled up. ### Time Time is a fundamental unit of measurement. It is often considered the fourth dimension in the space-time continuum. The only way time can be measured is to use some regular periodic motion and define one period the value of 1 unit. The unit time is 1 second. In the laboratory we use stop watch to measure the time. Time is often denoted as the symbol _t_. ### Distance or length Distance or length is a fundamental unit of measurement. It is one of three dimensions in space. The only way distance can be measured is to establish some arbitrary length and assign it a value of 1 unit. Distance is usually denoted by the symbol _d_. The meter is the unit of length in the metric system. A kilometer is simply 1000 meters. In the English system the inch is usually considered the unit of length, because larger units such as the foot or yard are made up of inches. Area is length time's width, with the units of square meters, square inches or such. Volume is length time's width time's height, the units of cubic meters, cubic inches or such. - 8- ## 1- Dimensional Measurements Using Vernier Calipers A caliper (British spelling also caliper) is a device used to measure the distance between two symmetrically opposing sides. A caliper can be as simple as a compass with inward or outward facing points. The tips of the caliper are adjusted to fit across the points to be measured, the caliper is then removed and the distance read by measuring between the tips with a measuring tool, such as a ruler. They are used in many fields such as metalworking, mechanical engineering, hand-loading, woodworking, and in medicine. ### 11-1 Uses of a vernier caliper It's used in measuring the external and internal dimensions and it is also used in the depth measurements. Description of a vernier caliper with labels for external, internal and depth measurements. ### 11-2 Parts of a vernier caliper: - **Outside jaws:** used to measure external diameter or width of an object. - **Inside jaws:** used to measure internal diameter of an object. - **Depth probe:** used to measure depths of an object or a hole. - **Main scale:** gives measurements of up to one decimal place (in cm). - **Main scale:** gives measurements in fraction (in inch). - **Vernier:** gives measurements up to two decimal places (in cm). - **Vernier:** gives measurements in fraction (in inch) - **Retainer:** used to block movable part to allow the easy transferring a measurement A variation to the more traditional caliper is the inclusion of a ... ; this makes it possible to directly obtain a more precise measurement. The vernier calipers can measure internal dimensions (using the uppermost ja Image of a vernier caliper with labels for the different parts. ### 11-3 How to read measurement from vernier caliper: The vernier calipers are useful for precise measurements of length and can be used to measure inside diameters, outside diameters and depth. Your instructor will demonstrate each type of measurement. The sliding scale of the vernier calipers is shown in the following figure and is read by adding the results from the major division, the minor division, and the aligned hash mark on the sliding scale. Image of a vernier caliper scale showing 3 minor divisions, 1 major division and the aligned mark. The total reading is 1.335 cm. ## Example: Image of a vernier caliper showing the reading. | | | | |---|---|---| | Major | A | 24 mm = 2.4 cm | | Minor | B | 0.62 mm | | Total | A+B | 24+0.62=24.62 mm | ## Exercise: Read the following measurement of the vernier calipers ### (A) Image of a vernier caliper showing the reading. - Accuracy = - Value = ### (B) Image of a vernier caliper showing the reading. - Accuracy = - Value = - 11- # 2- Dimensional Measurements Using the Micrometer Micrometers have 1.0 mm scale divisions above the reading line and 0.5 mm scale divisions below it. When taking a reading with a micrometer, tighten the thimble until the sample to be measured, at its widest point, can just barely slip from the anvil at spindle. Never tighten thimble so as to force the micrometer closed either on itself, or around a sample. There are 50 divisions on the thimble, and the thimble moves out along the sleeve by 0.5 mm in each rotation. Therefore, each division represents 0.01 mm (0.001 cm). Two complete rotations are therefore necessary to move the thimble a distance of 1 mm. When taking a reading, be careful to note whether the thimble is in its first or second rotation you can do this by examining whether the last visible scale division is above the reading line (first rotation) or below the reading line (second rotation). Note that the 11 mm mark is visible (above the reading line) but that there is an additional 5 mm scale marker visible (below the reading line). This means that the thimble is in its “second rotation” in this case this means that the final reading will be 11 mm + 0.5 mm (complete first rotation) + 0.33 mm (because the 33rd division lines up with the reading line). Image of a micrometer showing the labelled parts: Anvil, Spindle, Sleeve, Reading Line and Thimble. ### 2-1 How to read measurement from micrometer: - Take the reading from the line and suppose it A. - If the reading of the sleeve is visible, then B = 0.5 mm, if it is not visible put B = 0 mm as shown in figure B = 0.5 mm. - Take the reading of thimble (dial) C = 0.33 mm. - Total = A + B + C = 11 + 0.5 + 0.33 = 11.83 mm = 1.183 cm ## Example: Image of a micrometer with a reading showing A=7.00 mm, B=0.00 mm, C= 38 divisions * 0.01 mm/division = 0.38mm. - A = 7.00 mm - B = 0.00 mm - C = 38 × 0.01 = 0.38 mm -Total = A + B + C = 7.0 + 0.00 + 0.38 = 7.38 mm ## Exercise: ### (A) Image of a micrometer showing the reading. - A = - B = - C = - Total = A + B + C = ### (B) Image of a micrometer showing the reading. - A = - B = - C = - Total = A + B + C = - 13- # 3- Spherometer ### 3-1 Description of the Spherometer The spherometer is a precision instrument to measure the radius of a sphere. Its name reflects the way it is used to measure the radii of curvature of spherical surfaces of a lens. Image of a spherometer. In general the spherometer consists of: - A base circle of three outer legs placed at the corners of an equilateral triangle. - Through the center of the circle passes a screw forming a fourth leg which can be raised or lowered. - The head of the screw has a graduated disk of 100 divisions used to measure fractional turns of the screw. - A vertical scale used to measure the height of the curvature of the surface. The vertical scale division is 1 mm. ### 3-2 Measuring the radius of curvature R - The sperometer is placed on the slab of glass, and the center leg is screwed down until its point just touches the glass surface. In this position the zeros of the two scales should coincide. If this is not the case, however, the zero error must be found from the mean of several settings. - Screw up the central leg and place the spherometer with its three outer legs on the curved surface. - Screw down the center leg until it just touches the curved mirror, and the reading of the two scales is taken to be (h). - Press the spherometer on to a piece of paper, and the average distance (l) between the center and outer legs obtained. - Repeat step (4) several times and take the average of readings. 6- Determine the radius of curvature from the relation $$R = \frac{a^2}{2h} + \frac{h}{2}$$ $$R = \frac{6h}{2} $$ ## Experimental results: - Zero reading = - Readings of _h_ = - Average readings of _h_ = - Readings of _l_ = - Average readings of _l_ = - Radius of curvature $$R = \frac{a^2}{2h} + \frac{h}{2}$$ $$R = \frac{6h}{2} $$ Since, the focal length of curvature surface _f_ $$ f = \frac{R}{2}$$ Power of the curvature surface _P_ $$P = \frac{100}{f}$$ - 15 - # Experiment No. (2) ## Free Fall ### Objective: Determination of the acceleration due to gravity (g) using the free fall method. ### Theory: When air resistance is negligible all bodies near the earth's surface fall with the same constant acceleration denoted by the symbol _g_. Thus any object which is moving and being acted upon only by the force of gravity is said to be "free falling". The displacement of the body undergoing motion with constant acceleration can be described by the following equation: $$r = V_{0}t + \frac{1}{2}at^2$$ Where _r_ is the distance moved by the body, _V0_ is its initial velocity, _a_ is the constant acceleration of motion, and _t_ is the time elapsed. If the motion is conducted under the effect of the acceleration of gravity, equation ( ) becomes: $$Y = V_{0}t + \frac {1}{2}gt^2$$ If the object is dropped from rest, its initial velocity _V0_ is equal to zero and equation ( ) becomes: $$Y = \frac{1}{2}gt^2$$ According to equation ( ) a relation between the distance of the free falling on the y-axis and the square of the time elapsed on the x-axis is straight line passing with the origin as shown in Fig. ( ). The slope of this straight line gives the half of the acceleration of gravity, _g_. Image of a graph showing _g_ vs _t^2_ with a linear relation. ### Apparatus: A free falling body instrument consisting of: a metallic meter ruler, a simple digital timer, two photo gates and steel ball (falling body of the experiment) as shown in Fig. ( ). Image of the apparatus. ### Experimental procedure: - Switch on the digital timer. - Choose a suitable height _Y_, say 100 cm from the upper photo gate to the second photo gate. - Put the key of the digital timer at attract and carefully place the steel ball on the lower end of the electromagnet. - Put the start key at release, the ball then falls freely under the effect of gravity into the basket passing through the photo gates. - After the sphere leaves the electromagnet, there are three times appearing on the screen of the timer. The first one () refers to the time of falling from the point of release to the first photo gate while the second time ( ) is that of motion from the start point to the second photo gate. The difference _t_ ( - ) is the third time that is appears on the screen. - Read the time, _t_ of the free fall as indicated on the screen of the digital timer. Record, _Y_ and time, _t_ in the provided table. - Take at least three readings of the time at the distance, _Y_ and take the average. - Repeat the above steps by changing the height _Y_ and find in each case the corresponding time, _t_. - Plot a graph between the height _Y_ and the square of the average of the corresponding times of the free falling _t^2_ on the graph paper. - Find the slope of the straight line from which calculate the value of the acceleration of gravity, _g_ using the relation: $$g = 2xslope$$ - 18 - cm/sec2 ## Experimental results: | Y (cm) | t1 (sec) | t2 (sec) | t3 (sec) | tav (sec) | t^2 (sec^2)| |---|---|---|---|---|---| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - slope = - g = 2xslope = - 19 - # Experiment No. (3) ## Simple Pendulum ### Objective: Determination of the acceleration due to gravity using a simple pendulum. ### Theory: A simple Pendulum is a small bob tied to the end of a long string of length _L_ cm whose other end is fixed. When displaced with a small angle _θ_ from its equilibrium position, it executes Simple Harmonic Motion (S.H.M.). Image of a pendulum showing the oscillation direction with labelled parts _O_, _θ_ and _L_ . Also image of the bob showing its position at different times and its weight components with labels _m_, _mg_, _mg sinθ_ and _mg cosθ_. If _m_ is the mass of the bob and _θ_ is the displacement, the forces acted on _m_ are theweight _mg_, where _g_ is the acceleration of gravity, and the tension of the string _T_ as shown in Fig.( ). By analyzing the weight _mg_ into two components: - In direction of string = _mg cosθ_ which is equal to tension _T_. - In perpendicular direction of string = _mg sinθ_. Thus the force which is acted on _m_ is given by $$F = - mg sin θ$$ The negative sign means that the bob is directed toward the equilibrium position. Since _θ_ is small, therefore _sin θ_ ≈ _θ_, Equation () becomes $$ F = - mg θ$$ Applying Newton's second law $$F = ma$$ (where _a_ is the magnitude of the mass's acceleration), to the perpendicular component of string we get $$F = ma$$ From equations ( ) and ( ) $$a = - g θ$$ but, _θ_ = _X/L_, therefore $$a = -g(X/L)$$ On the other hand the equation of S.H.M. is known as $$a = -ω^2X$$ where _ω_ is known as the angular frequency. Thus by comparing equations ( ) and ( ) we get $$ω^2 = g/L$$ since _ω_ =2 π_f_ and _f_ is the frequency. In addition $$f = 1/t$$ where _t_ is the periodic time for one revolution. Substituting from equation ( ) into equation ( ) we have $$t^2 = \frac{4\pi^2L}{g}$$ If we plot _t2_ on the x-axis and _L_ on the y-axis, we get straight line passes through the origin and has a slope $$ \frac{4\pi^2}{g}$$ (Fig. ). Substituting in equation ( ) we can determine the acceleration of gravity. Image showing a graph between _L_ and _t^2_ . Labels are _t^2_ (sec^2) and _L_ cm. The slope of the line is _BC/AC_. ### Apparatus: Simple pendulum – stand and clamp – metal rule – stop watch. ### Experimental procedure: - Measure the length of the pendulum from the hanging point to the center of the mass. - NOTE: this length must be not less than 30 cm (add the radius of the bob). - Move the bob a small distance horizontally, then find the time of 10 complete cycles _t10_ sec, remember that the angle must be very small. - Calculate the time of one complete revolution _t_ = _t10_/10 sec. - Square the time of one complete cycle, _t2_ sec². - Repeat steps 2, 3 and 4 for different lengths _L_ cm. - Write down your readings in the provided table. - Plot a graph between _L_ (x-axis) and _t2_ (y-axis). - Determine the slope, and then calculate _g_. ## Experimental results: | L cm | reading (1) | t10 sec (reading (2) | reading (3) | Average t10 sec | t = t10/10 sec | t^2 sec^2 | |---|---|---|---|---|---|---| | 30 | | | | | | | | 40 | | | | | | | | 50 | | | | | | | | 60 | | | | | | | | 70 | | | | | | | | 80 | | | | | | | | 90 | | | | | | | | 100 | | | | | | | - slope = $$g = \frac{4 \pi^2}{slope}$$ - 25 - ## k = $$k = \frac{F}{L} = \frac{1}{slope}$$ - 26 - # Experiment No. (4) ## Verification of Boyle's Law of Gases ### Objective: Studying the relationship between the volume and the pressure of a given gas (air) at constant temperature. ### Theory: The pressure (P), volume (V), and temperature (T) of a gas are related to each other by the general gas equation which states that: $$ \frac{PV}{T} = \frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2}=constant $$ and so on where _P_, _V_, and _T_ represent different sets of pressure, volume and temperature of certain mass of the gas. Boyle’s law is a specific case of this equation where the temperature is constant (isothermal) i.e. _T₁=T2_ thus we have: $$P_1V_1=P_2V_2=P_3V_3=... $$ and so on This means that _PV_= constant and this constant is equal to nRT. Where: - n: is the number of moles of the gas - R: is the universal Gas Constant = 8.315 j/k.mole - T: is the temperature of the gas in Kelvin, _T_(°K)=_T_(°C)+273. Then: $$PV=nRT$$ Or in other form: $$P = (nRT)\frac{1}{V}$$ Boyle’s law states that: "The pressure of an enclosed gas is inversely proportional to its volume at a constant temperature". Graphically Boyle’s law is represented in Fig. ( ) Image showing two graphs for P vs V. The first is linear and the second is curved. ### Apparatus: Syringe - interface computer - pressure sensor ### Experimental procedure: - Connecting the computer to the interface and placing the pressure sensor in it. - Open the data stadio program and choose the creat experiment. We will notice the presence of pressure in the existing data. - We enter the set up from which we activate the keep data value to add the volume and activate it and write the volum and its unit ml. - We pull a table from display, press it, then put another box, the size. - We draw a graph from the display to the graph and place the volume on the x axis and pressure on the y axis. - Put the syringe in the pressure sensor. - We press start and make the syringe volume 25ml then keep to record the first value. - We repeat this step several times for different sizes 23,21,19, ml .... we find the graph an inverse relationship. - 29 - # Introduction to Heat ## Heat, thermal energy, and temperature ### Heat Heat is a change in thermal energy. Thermal energy being moved from one object to another. Heat is energy, so the SI unit is joules (J). The usual symbol used for heat in equations is _Q_. ### Thermal energy Thermal energy is energy on an atomic or molecular level. This energy can be kinetic energy, or potential energy. Because there are forces between the atoms and molecules in a substance, movement against these forces can store energy as potential energy. Two examples of this, thermal expansion and phase changes are considered below. ### Temperature Temperature is a measure of the kinetic energy per atom/molecule. When there is no motion, there is no kinetic energy, and the temperature is absolute zero. (0 K, or -273°C). The SI unit of temperature is the Kelvin. Convert from degrees Celsius to Kelvin by adding 273. A temperature difference _ΔT_ is the same in Kelvin or degrees Celsius. ### Heat and temperature There is a difference between temperature and heat. A standard of temperature is a measure of movement of molecules of the body. The heat is the body's energy gained from the movement of its molecules. ### The relationship between internal energy and temperature The body in turning the heat energy, increases the capacity of vibrations of molecules and far apart, thus increasing the speed of particles and increases the kinetic energy of the particles and therefore increases the internal energy of the material and the temperature rises, and vice versa. - 31 - ## Effects of heat Most of the materials expand with heat and shrink when cooled. When heated material gains energy to make particles move faster and farther, it occupies more space. When the temperature changes enough, the substance turns from the case to the other. If a solid is heated to the melting point, it melts, and if a liquid is heated to a high temperature, it boils and turns into a gas or vapor. ### Heat capacity The amount of heat needed to raise the temperature of any particular amount of a substance by 1°C. ### Specific heat How much does the temperature rise when a certain amount of heat is added to a substance? This is measured by the specific heat capacity, or specific heat. In SI units, the specific heat is the amount of heat needed to raise the temperature of one kilogram by 1 K (or 1°C). The amount of heat needed to raise the temperature of a mass _m_, with a specific heat _c_, by _ΔT_ is: $$Q = mc ΔT$$ The specific heat of a substance depends on what the substance is. For water, _c_ = 4186 J/kg.K. ### Heat transfer Heat will flow from a hot region to a cold region by three ways: 1. **Conduction:** It occurs in solid bodies through which heat flows from a hot area to a cold one. 2. **Convection** It occurs in gases and liquids. 3. **Radiation** It is the only way to transfer heat through a vacuum. - 32 - # Experiment No. (5 ) ## Latent Heat of Fusion of Ice ### Objective: Determination of the latent heat of fusion (Lf). ### Theory: When ice melts and begins to change into water the temperature remains constant although the ice continuously gains heat. The amount of heat which is absorbed during a change of ice state into water without rise in temperature is called the latent heat of fusion, also called heat of transformation, which is defined as: "The amount of heat required changing 1 gm of ice into water at 0°C". When an ice cube of mass *m1*, assumed to be at 0°C, is placed in a calorimeter containing a mass of water *mw* at initial temperature *T1*, the ice cube melts. After the melting, the temperature of the system is *Tf*. The ice will be converted into water and gain some heat (energy) from the water and the calorimeter. Therefore, The heat gained by ice = The heat lost by water and calorimeter $$m_1c_i (Tƒ– 0 ) + m_iL_f = (m_wc_w +m_cc_c) (T_1 – T_f)$$ $$L_f = \frac{(m_wc_w +m_cc_c)(T_1 – T_f) - m_1c_i(T_f – 0)}{m_i}$$ where - *Lf*: latent heat of fusion. - *Cw, Ci, Cc*: specific heat of water, ice and calorimeter respectively. - *mw, mi, mc*: mass of water, ice and calorimeter respectively. - *T₁,Tf*: initial and final temperatures of water (after ice melts in water) respectively. ### Apparatus: Image showing two containers. The left container is labelled *(a)*, with a thermometer in the liquid. The right container is labelled *(b)* and has ice inside the liquid. Ice - calorimeter – thermometer – sensitive balance – blotting paper. ### Experimental procedure: - Determine the mass of the calorimeter empty and dry *mc* (gm). - Fill 1/2 of calorimeter with water and determine the mass of water by weighing the calorimeter with its_contents_ *mc+w*, then determine the mass of the water *mw* = *mc+w* -*mc* (gm). - Warm the calorimeter with its_contents_ 5°C above the room temperature and record the temperature *T₁*(°C) Fig. (1-a). - Put small pieces of ice after being carefully dried with filter paper (blotting paper) in the calorimeter, as shown in Fig. (1-b), till the temperature is 10°C less than *T₁* (to correct for the heat lost or gained by radiation). (Be careful to stir until all the ice is melted before adding more ice). - Stir gently with the thermometer and notice the temperature until a minimum is reached and record its value let it be *Tƒ*(°C). - Find the mass of ice *m₁* (gm) turned into water by weighing the calorimeter with its contents *mc+i+w*. Then *m₁* = *Mc+i+w* - *Mc+w* (gm). - Calculate the latent heat of fusion *L₁*, (cal./gm) using equation ( ). ## Experimental results: - Mass of the calorimeter empty *mc* = - Mass of the calorimeter and water *mc+w* = - Mass of the water *mw* = - Mass of the calorimeter with water and ice *mc+w+i* = - Mass of ice *m₁* = - Initial temperature *T₁* = - Final temperature *Tƒ* = - Specific heat of water *Cw* = cal/gm°C - Specific heat of ice *Ci* = - Specific heat of calorimeter *Cc* = - Latent heat of fusion *Lƒ* = - 35 - - 36 - # Experiment No. ( 6 ) ## Gay Lussac's Law Pressure – Temperature Dependence of a Gas ### Objective: Studying how the pressure of a gas changes with temperature at constant volume. ### Theory: Gas Lussac's Law is the third one leading up to the ideal gas law. The first is Boyle's Law, which gives the relationship between volume and pressure, and the second is Charle's Law, which gives the relationship between volume and temperature. Gay Lussac's Law states that "the pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature". Simply if a gas's temperature increases then so does its pressure, provided the mass and volume of the gas are held constant. The law has a particularly simple mathematical form if the temperature is measured in Kelvin. The law can then be expressed mathematically as $$PaT$$ or $$P/T = K$$ where - _P_ is the pressure of the gas - _T_ is the temperature of the gas (measured in Kelvin's) - _K_ is a constant This law holds true because temperature is a measure of the average kinetic energy of a substance, as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure. - 37 - For comparing the same substances under two different sets of conditions the law can be written as $$P_1/T_1 = P2/T2$$ or $$P_1 T_2 = P_2 T_1$$ where _P₁_ and _T₁_ are the original values of the gas state, while _P2_ and _T2_ represents its final state values. From equation ( ), representing _T_ on the x-axis and _P_ on the y-axis, we get straight line passing through the origin which verify Gay Lussac's Law. On the other hand, from the general law of ideal gases we have _P V_ =nRT $$P/T=nR / V $$ where _R_ is universal constant and _n_ is the number of moles, hence the slope of the straight line dependence between _T_ & _P_ is equal to _nR/V_. If the volume of the gas in a container is known, the number of moles _n_ of the trapped air can be estimated. Since _n_ = _m/M_ where _m_ is the mass of the gas and _M_ is the molar weight in (g/mol), known that the density of air is 1.294 kg/m³, the value of _M_ can be calculated. ### Apparatus: Electrical heater – aluminum boiler – Digital temperature – small gas reservoir – pressure gauge stand base with clamp – stand stainless rod as shown in fig.( ). Image of the apparatus. ### Experimental Procedure: - Fill the steam generator with water. - Raise the temperature of the water. - Measure the temperatures of the water gradually _t_ and the pressure of the trapped gas (P). - Repeat step 3 until reaching the boiling point of water. 5- Tabulate your results in the providing table. - Plot a relation between _T_ = _t_ °C + 273 on the x-axis and _P_ on the y-axis. - Verify Gas Lussac's Law. ## Experimental Results: | t°C | T K | P | |---|---|---| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - 40 - -