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Questions and Answers
The slope of a graph plotting mass (m) against volume (V) for a substance represents which property?
The slope of a graph plotting mass (m) against volume (V) for a substance represents which property?
- Specific gravity
- Density (correct)
- Volume
- Weight
Which of the following is a factor affecting the density of a substance?
Which of the following is a factor affecting the density of a substance?
- The color of the substance
- The atomic weight (correct)
- The ambient pressure
- The shape of the container
What is the dimensional formula for density?
What is the dimensional formula for density?
- $MLT^{-2}$
- $M^{-1}L^{3}T^{0}$
- $ML^{-3}T^{0}$ (correct)
- $M^{2}L^{-3}T^{0}$
If you mix two liquids with densities $\rho_1$ and $\rho_2$ and volumes $V_1$ and $V_2$ respectively, what is the density of the mixture, assuming the volumes are additive?
If you mix two liquids with densities $\rho_1$ and $\rho_2$ and volumes $V_1$ and $V_2$ respectively, what is the density of the mixture, assuming the volumes are additive?
How is the relative density of a substance defined in terms of its density and the density of water?
How is the relative density of a substance defined in terms of its density and the density of water?
The relative density of a material is measured under which condition?
The relative density of a material is measured under which condition?
What is the relationship between the mass of a material and its density when the volume is kept constant?
What is the relationship between the mass of a material and its density when the volume is kept constant?
Given a mixture of 50 $m^3$ of water with a density of 1000 $kg/m^3$ and 40 $m^3$ of liquid with a density of 790 $kg/m^3$, what is the density of the resulting mixture?
Given a mixture of 50 $m^3$ of water with a density of 1000 $kg/m^3$ and 40 $m^3$ of liquid with a density of 790 $kg/m^3$, what is the density of the resulting mixture?
If the relative density of a certain type of wood is 0.6, what is the density of this wood in $kg/m^3$?
If the relative density of a certain type of wood is 0.6, what is the density of this wood in $kg/m^3$?
If the relative density of a piece of wood is 0.6, then what is the mass of a 0.1 $m^3$ piece of this wood?
If the relative density of a piece of wood is 0.6, then what is the mass of a 0.1 $m^3$ piece of this wood?
The average force acting perpendicularly on a unit area surrounding a point is the definition of what?
The average force acting perpendicularly on a unit area surrounding a point is the definition of what?
The pressure exerted by a force $F$ acting on an area $A$ at an angle $\theta$ to the area's normal is given by:
The pressure exerted by a force $F$ acting on an area $A$ at an angle $\theta$ to the area's normal is given by:
What are the dimensions of pressure?
What are the dimensions of pressure?
If several surfaces with different areas are subjected to different forces, on which surface is the pressure exerted the maximum?
If several surfaces with different areas are subjected to different forces, on which surface is the pressure exerted the maximum?
A fish tank with a base area of 1000 $cm^2$ contains water with a weight of 4000 N. If the tank is placed on a horizontal surface, calculate the pressure of the water at the bottom of the tank.
A fish tank with a base area of 1000 $cm^2$ contains water with a weight of 4000 N. If the tank is placed on a horizontal surface, calculate the pressure of the water at the bottom of the tank.
A force of 15 N acts on an area of 2 $cm^2$ at an angle of 30° with respect to the normal. What is the pressure exerted on the area?
A force of 15 N acts on an area of 2 $cm^2$ at an angle of 30° with respect to the normal. What is the pressure exerted on the area?
What is the formula for calculating the pressure at a certain depth inside an open container with liquid.
What is the formula for calculating the pressure at a certain depth inside an open container with liquid.
The force exerted by a liquid on the bottom of a container depends on which factors?
The force exerted by a liquid on the bottom of a container depends on which factors?
In analyzing the pressure at different points inside a lake, the graph represents the relation between the pressure (P) and depth (h). What does the value at h=0 represent?
In analyzing the pressure at different points inside a lake, the graph represents the relation between the pressure (P) and depth (h). What does the value at h=0 represent?
If you analyze the pressure at different points inside a lake and graph it, what does the slope of the graph represent if you plot pressure (P) against depth (h)?
If you analyze the pressure at different points inside a lake and graph it, what does the slope of the graph represent if you plot pressure (P) against depth (h)?
The pressure at the bottom of a high dam depends on which factor?
The pressure at the bottom of a high dam depends on which factor?
Which of the following graphs represents the total external pressure acting on a submarine at different depths below the surface of the sea?
Which of the following graphs represents the total external pressure acting on a submarine at different depths below the surface of the sea?
Connecting vessels are an application of pressure, which of the following is true for them?
Connecting vessels are an application of pressure, which of the following is true for them?
A U-tube includes two liquid, one of them being water. What statement is true for the relative density?
A U-tube includes two liquid, one of them being water. What statement is true for the relative density?
In a barometer, what variables can be used to approximate the height of a mountain?
In a barometer, what variables can be used to approximate the height of a mountain?
Which of the following increases the height above sea level?
Which of the following increases the height above sea level?
If you submerge a capillary tube in water, what factor will affect the pressure inside?
If you submerge a capillary tube in water, what factor will affect the pressure inside?
What is measured using a manometer?
What is measured using a manometer?
In a mercury manometer, what happens to the pressure if the liquid level in the free end branch changes compared to the level on the other side?
In a mercury manometer, what happens to the pressure if the liquid level in the free end branch changes compared to the level on the other side?
The height in two liquids are different when at equilibrium inside a U-shaped tube, so what can you infer about its densities?
The height in two liquids are different when at equilibrium inside a U-shaped tube, so what can you infer about its densities?
When is Pascal's Principle applicable?
When is Pascal's Principle applicable?
In hydraulic presses, what quantity is being multiplied?
In hydraulic presses, what quantity is being multiplied?
In an ideal hydraulic press with pistons at the same horizontal level, how does the force produced at the big piston compare to the force acting on the small piston?
In an ideal hydraulic press with pistons at the same horizontal level, how does the force produced at the big piston compare to the force acting on the small piston?
If the radii are 8/3, what is the work due to the motion?
If the radii are 8/3, what is the work due to the motion?
What best describes Boyles Law
What best describes Boyles Law
If the volume of a gas is 2 liters at 2 atm, what does it become when the pressure decreases to 1 atm at a constant temperature?
If the volume of a gas is 2 liters at 2 atm, what does it become when the pressure decreases to 1 atm at a constant temperature?
An amount of gas of volume 350 $cm^3$ at a pressure of 2 atm is expanded, what is the volume at 1 atm?
An amount of gas of volume 350 $cm^3$ at a pressure of 2 atm is expanded, what is the volume at 1 atm?
A gas has an initial density of 32 g/L when the pressure is at 760 mm Hg. If pressure is decreased to 570 mm Hg, what does its density become?
A gas has an initial density of 32 g/L when the pressure is at 760 mm Hg. If pressure is decreased to 570 mm Hg, what does its density become?
What best described Charle's law?
What best described Charle's law?
Where does the volume stay constant?
Where does the volume stay constant?
If an amount of gas is 450 $cm^3$ at a temperature of 273 K, what volume does it measure at 364K?
If an amount of gas is 450 $cm^3$ at a temperature of 273 K, what volume does it measure at 364K?
What best describes volume expansion?
What best describes volume expansion?
If the pressure of a quantity of gas is 59.8 cm Hg, what is the pressure if the volume stays constant?
If the pressure of a quantity of gas is 59.8 cm Hg, what is the pressure if the volume stays constant?
In the context of gas laws, what does the general gas law describe?
In the context of gas laws, what does the general gas law describe?
The volume of a gas at 27°C under a pressure of 60 cm Hg is 380 cm. Find its volume at the (STP)
The volume of a gas at 27°C under a pressure of 60 cm Hg is 380 cm. Find its volume at the (STP)
If you graph two equal masses of the same gas, what do you infer knowing if volume 1 is greater than volume 2?
If you graph two equal masses of the same gas, what do you infer knowing if volume 1 is greater than volume 2?
Flashcards
Density
Density
Mass per unit volume of a substance.
Slope of Density Graph
Slope of Density Graph
The change in mass divided by the change in volume on a graph.
Density of a Mixture
Density of a Mixture
Density of a mixture is the total mass of the mixture divided by the total volume of the mixture.
Relative Density
Relative Density
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Pressure
Pressure
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Pressure in a Liquid (Open)
Pressure in a Liquid (Open)
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Pressure in a Liquid (Closed)
Pressure in a Liquid (Closed)
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Force Exerted on Container Bottom
Force Exerted on Container Bottom
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Barometer
Barometer
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Pressure in Horizontal Plane
Pressure in Horizontal Plane
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Pascal's Principle
Pascal's Principle
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Hydraulic Press
Hydraulic Press
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Hydraulic Press Advantage
Hydraulic Press Advantage
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Boyle's Law
Boyle's Law
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Charles's Law
Charles's Law
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Pressure Law
Pressure Law
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General Gas Law
General Gas Law
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Study Notes
Density
- Density is the mass per unit volume of a substance
- Density is represented by ρ and Volume is represented by Vol
- The mathematical relation for density is ρ = m / Vol
- Density is a scalar quantity
- The measuring unit for density is Kg/m³
- The dimensional formula for density is ML⁻³T⁰
Graph of Density
- The slope of the graph (Δm / ΔVol) equals density (ρ)
Factors Affecting Density
- Atomic weight or molecular weight
- Distance between atoms or molecules
Density Equations
- m_mix = m₁ + m₂ + ...
- ρ_mix(V_ol)_mix = ρ₁(V_ol)₁ + ρ₂(V_ol)₂ + ...
- (V_ol)_mix = (V_ol)₁ + (V_ol)₂ + ...
Volume Formulas
- Sphere: V_ol = (4/3)πr³
- Cylinder: V_ol = πr²h
- Rectangular prism: V_ol = hlw
Relative Density
- ρ_relative = (ρ_material) / (ρ_water) at the same temperature
- ρ_relative = (m_material) / (m_water) at the same volume and temperature
- ρ_relative = (W_material) / (W_water) at the same volume and temperature
Pressure
- Pressure is the average force acting perpendicular to the unit area surrounding a point
- The measuring unit for pressure is Pascal (Pa).
Pressure Equivalents
- 1 Pascal (Pa) is equivalent to Kg⋅m⁻¹⋅s⁻²
- 1 Pascal (Pa) is equivalent to N/m²
- 1 Pascal (Pa) is equivalent to J/m³
Pressure Formulas
- Force perpendicular to the area: P = F/A = mg/A
- Force makes angle θ with the area: P = (F sin θ)/A
- Force makes angle θ with the normal of area: P = (F cos θ)/A
- A is the area
Pressure Dimensions
- Pressure dimensions are ML⁻¹T⁻²
Pressure at a Point Inside a Liquid
- Opened to air: P = ρgh + Pa
- Closed: P = ρgh
- ΔP/Δh = ρg, which represents the slope
Force Calculation in Liquids
- Force at the bottom of the container: F = ρghA = ρgV_ol
- Force on one of the vertical faces of the container: F = ρg * (1/2)hA = (1/2)ρghA = (1/2)ρgV_ol
Atmospheric Pressure
- Atmospheric pressure is measured in Pascal (Pa).
- Denoted as Pa.
- It is directly proportional to average density of air and acceleration due to gravity
- It is inversely proportional to temperature, and height above sea level
- 1.013 × 10⁵ N/m² equals 1.013 × 10⁵ Pascal
- 1.013 × 10⁵ N/m² equals to 1.013 bar
- 1.013 × 10⁵ N/m² equals 1 atm
- 1.013 × 10⁵ N/m² equals 0.76 mHg
- 1.013 × 10⁵ N/m² equals 76 cmHg
- 1.013 × 10⁵ N/m² equals 760 mmHg
Applications
- Connecting vessels: Pa = PB = PC = PD = PE and ha = hB = hC = hD = hE
- Mercury barometer: PA = PB = Pa and Pa = ρHgghHg
U-Tube Manometers
Structure of U-Tube
- U-shaped tube
Idea Behind U-Tube
- Pressure is the same at all points in the same horizontal plane in a static homogeneous liquid
Uses of U-Tube
- Comparing the density of two liquids
- Determining the density of a liquid by knowing the density of another liquid
- Determining the relative density of a liquid that does not mix with water (immiscible liquid)
U-Tube Types
- More than two liquids: P_A = P_B, ρ₁h₁ = ρ₂h₂ + ρ₃h₃
- Two liquids: P_A = P_B, ρ₁h₁ = ρ₂h₂
Barometer
- A glass tube of length 1 m opened at one end
- A tank of suitable volume
- A suitable volume of mercury
Idea
- Pressure is the same at all points in the same horizontal plane in a static homogeneous liquid.
- Pressure at point (A) = Pressure at point (B).
Uses
- Measuring atmospheric pressure
- Determining the height of a mountain or a building
Formulas
- Pa = PA = ρgh
- ΔP(mercury) = ΔP(air) is PHg g (h₁ - h₂) = Pair ghmountain
Capillary Tube
Formulas
- ρ = Pa - h
- ρ = Pa + h
- ρ = Pa
Manometer
- Structure: Includes a gas
- Idea: Pressure at all points in the same horizontal plane in a static homogeneous liquid is the same.
- Types: Water manometer and mercury manometer
Uses
- Measuring the pressure of enclosed gas
- Measuring the difference between the pressure of enclosed gas and the atmospheric pressure
Formulas
- If the liquid level in the free end branch is the same as the level in the other branch, then: ΔP = 0
- If the liquid level in the free end branch is higher than the liquid level in the other branch, then: ΔP = + ρgh (N/m²) or ΔP = +h (cmHg) if using mercury
- If the liquid level in the free end branch is lower than the liquid level in the other branch, then: ΔP = -ρgh or ΔP = -h (cmHg) if using mercury
Pascal's Principle
Formulas
- Two points are at different levels: P₁ = P₂, f/a + ρgh = F/A
- Two pistons are at the same level: P₁ = P₂, f/a = F/A
Mechanical Advantage of Hydraulic Press
- η = A/a = R²/r² = y₁/y₂
- Efficiency = (Work done at big piston) / (Work done at small piston) = (Fy₂)/(Fy₁)
Laws of Gases
Boyle's Law
- At constant temperature, the volume of a fixed mass of gas is inversely proportional to the pressure of the gas
- P(Vol) = const (constant)
- P₁/P₂ = (Vol)₂/(Vol)₁
Charles's Law
- At constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature on Kelvin scale
- (Vol)/T = Const (constant)
- (Vol)₂/(Vol)₁ = T₂/T₁
Pressure Law
- At constant volume, the pressure of a fixed mass of gas is directly proportional to its temperature on Kelvin scale
- PVol = Const (constant)
- P₁/P₂ = T₁/T₂
General Gas Law
- P₁ / (ρ₁T₁) = P₂ / (ρ₂T₂)
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