Thermal Properties of Matter PDF

### 7. Thermal Properties of Matter 02) Answer the following questions: - i) Clearly state the difference between heat and temperature. - **Ans:** - Heat is a form of energy transferred between a system and its surroundings by virtue of their temperature difference. - Tempera...

### 7. Thermal Properties of Matter 02) Answer the following questions: - i) Clearly state the difference between heat and temperature. - **Ans:** - Heat is a form of energy transferred between a system and its surroundings by virtue of their temperature difference. - Temperature measures the degree of hotness of an object. - SI unit of heat is joule (J) while SI unit of temperature is Kelvin (K) or Celsius (°C). - Dimensions of heat are [L²M¹T⁻²] while dimensions of temperature are [L⁰MTK⁻¹]. - Heat is measured with the help of a calorimeter, while temperature is measured with the help of thermometers. - ii) How a thermometer is calibrated ? - **Ans:** - For calibration of a thermometer, a standard temperature interval is selected between two easily reproducible fixed temperatures. - The next step is to sub-divide this standard temperature interval into sub-intervals called as degree of temperature. - Last step is to assign numerical values to these fixed points and also to the number of divisions between them. This procedure sets up an empirical scale for temperature. - iⅱ) What are different scales of temperature? What is the relation between them? - **Ans:** The different scales of temperature are: - Celsius scale - Fahrenheit scale - Relation between them: $T_F-32/180 = T_C-0/100$ - iv) What is absolute Zero? - **Ans:** - The temperature at which the pressure of a gas would be zero is called absolute zero of temperature. - This temperature is -273.15 °C. - In practice, absolute zero temperature or lower than that is not possible to achieve. - v) Derive the relation between three coefficients of thermal expansion. - **Ans:** - Consider a square plate of side l_0 and l_T at 0°C and T °C respectively. - We know: - l_T = l_0 (1+αT) - (1) - A_T = A_0 (1+βT) - (2) - V_T = V_0 (1+γT) - (3) - **Relation between β and α:** - Area of plate at 0°C A_0 = l_0² - (4) - Area of plate at T°C A_T = l_T² - (5) - Using eqn (1) l_T = l_0 (1+αT) - Squaring on both sides: l_T² = l_0² (1+αT)² - Using eqn (4) and (5) - ∴ A_T = A_0 (1+αT)² - Substitute A_T from eqn (2): - A_0 (1+βT) = A_0 (1+αT)² - 1+βT = 1+2αT+α²T² - Since values of α are very small, term of higher powers α²T² can be neglected. - 1+βT = 1+2αT - βT = 2αT - ∴ β = 2α - (I) - **Relation between γ and α:** - Volume of plate at 0°C V_0 = l_0³ - (6) - Volume of plate at T°C V_T = l_T³ - (7) - Using eqn (1) l_T = l_0 (1+αT) - Taking cube on both sides: l_T³ = l_0³(1+αT)³ - Using eqn (6) & (7): V_T = V_0 (1+αT)³ - Substitute V_T from eqn (3): - V_0 (1+γT) = V_0 (1+αT)³ - 1+γT = 1+3αT + 3α²T² + α³T³ - Since values of α are very small, term of higher powers 3α²T², α³T³ can be neglected. - 1+γT = 1+ 3αT - γT = 3αT - ∴ γ= 3α - α=γ/3 - (II) - From (I) & (II) we get: - α = β/2 = γ/3 - vi) State applications of thermal expansion - **Ans:** Applications of thermal expansion: - i) **Thermometers:** In thermometers, thermal expansion is used in temperature measurements. Due to expansion of mercury, the liquid level rises and shows temperatures. - ii) **Removing tight lids:** To open the cap of a bottle that is tight, immerse it in hot water. Metal cap expands and becomes loose. It would now be easy to turn it to open. - iii) **Fit steel wheel on axle:** The steel wheel is heated to expand. Expanded wheel easily fits over axle. Then wheel is cooled so that it contracts and fits tightly over the axle. - vii) Why do we generally consider two specific heats of a gas? - **Ans:** - i) If a gas is heated at constant pressure then its volume changes. - ii) During expansion, volume increases. This is possible when some work is done on surrounding. - iii) So additional heat is required for doing some work on the surroundings. - iv) As a result of it, specific heat at constant pressure (Sp) is greater than specific heat at constant volume. Therefore, two specific heats of a gas are considered. - viii) Are freezing point and melting point same with respect to change of state? Comment. - **Ans:** Yes, freezing point and melting point mark same temperature. - Freezing point is the temperature at which liquid gets converted into solid. - Melting point is the temperature at which solid gets converted into liquid. - ix) **Define Sublimation:** The change from solid state to vapour state without passing through the liquid state is called Sublimation. - **Triple point:** Triple point is the unique value of pressure and temperature at which all the three states of matter (solid, liquid and vapour) coexist in equilibrium. - x) Explain the term 'Steady state'. - **Ans:** - i) When one end of a metal rod is heated, the heat flows by conduction from hot end to the cold end. - ii) As a result, the temperature of every section of the rod starts increasing. - iii) Under this condition, the rod is said to be in variable temperature state. - iv) After some time, the temperature at each section of the rod becomes steady i.e. does not change even when the rod continues to receive heat. - v) Temperature of each cross-section of the rod is constant but not the same. This is called steady state condition. - xi) Define coefficient of thermal conductivity. Derive its expression. - **Ans:** - Coefficient of thermal conductivity of a material is defined as the quantity of heat that flows in one second between the opposite faces of a cube of side 1 m, the faces being kept at a temperature difference of 1°C (or 1 K). - **Expression:** Under Steady state condition, the quantity of heat Q flowing from hot face to cold face is: - i) directly proportional to cross-sectional area A of face - ii) directly proportional to temperature difference between two faces (T₁-T₂) - iii) directly proportional to time t for which heat is flowing - iv) inversely proportional to distance x between the two faces. - Combining above four factors, we get: - Q α A (T₁-T₂) t/x - Q = KA (T₁-T₂) t/x - where k is constant called coefficient of thermal conductivity - ∴ K = Qx/A (T₁-T₂) t - xii) Give any four applications of thermal conductivity in every day life. - **Ans:** Four applications are: - i) Cooking utensils are made of metals but are provided with handles of bad conductor. - ii) Ice does not melt so rapidly in sawdust as it is bad conductor of heat. - iii) Electric iron has mica coating, which is good conductor of heat but bad conductor of electricity to protect from shock. - iv) Thick walls containing bricks are used in construction of cold storage rooms as bricks are bad conductor of heat. - xiii) Explain the term thermal resistance. State its SI unit and dimensions. - **Ans:** The opposition of a body to the flow of heat through it is called thermal resistance. - Thermal resistance R_T = x/KA = (T₁-T₂)/P_cond - where: - x is distance between two faces. - K is thermal conductivity. - A is cross-sectional area. - T₁-T₂ is temperature difference. - P_cond is rate of flow of heat - SI unit is Kcal/Cs or J/Cs. - Dimensions: [L⁻²M¹T³K¹] - xiv) How heat transfer occurs through radiation in absence of a medium? - **Ans:** - i) All objects possess thermal energy due to their temperature T (if T>OK) - ii) The rapid vibrations of molecules of hot body cause emission of electromagnetic waves. - iii) These electromagnetic waves carry energy with which travel with velocity of light. - iv) These thermal energy is transferred to molecules of cold body thereby increasing their vibrations, and its temperature rises. - v) Electromagnetic waves can travel in vacuum. Hence heat energy through radiation is achieved in absence of medium. - xv) State Newton's law of cooling and explain how it can be experimentally verified. - **Ans:** - **Statement:** The rate of loss of heat dT/dt of the body is directly proportional to the difference of temperature (T- T_0) of the body and the surroundings, provided the difference in temperatures is small. - **Verification:** - i) Fill the calorimeter upto two third of its capacity with the boiling water and fix a thermometer in it. - ii) Keep calorimeter vessel in constant temperature enclosure. - iii) Note the temperature on the thermometer at every one-minute interval until temperature of water decrease to about 25°C. - iv) Plot a graph of temperature (T) on Y axis against time (t) on X-axis. This graph is called cooling curve. - v) It is seen from graph that initially the rate of cooling is higher and then decreases as the temperature of water falls. - vi) Slope dT/dt is calculated at few temperatures. - vii) Plot graph of dT/dt against (T-T_o) where T_o is temperature of surrounding. - viii) The graph is a straight line passing through origin which verifies Newton's law of cooling. - xvi) What is thermal stress? Give an example of disadvantages of thermal stress in practical use? - **Ans:** - i) Consider a metallic rod of length L_i fixed between two rigid supports. - ii) If the temperature of rod is increased, then length of rod will increase due to thermal expansion. - iii) But the supports prevent expansion of rod. - iv) As a result, metallic rod exerts stress on the rigid supports. Such stress is termed as thermal stress. - **Disavantage:** Thermal stress can lead to fracture or deformation in substance. If gaps are NOT kept between railway tracts, then due to expansion of metal tracks thermal stress may be exerted. This may lead to bending of tracks. - xvii) Which materials can be used as thermal insulators and why? - **Ans:** - i) Lower the thermal conductivity, higher is the thermal resistance R_T. - ii) Materials with high thermal resistance R_T are a poor thermal conductor and is a good thermal insulator. - iii) Substances such as glass, wood, rubber, plastic etc. can be used as thermal insulators.