boyle’s law and charles law

What is Charles’ Law in Physics?

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What is the Relationship Between Temperature and Volume of a Gas

 

  1. A woman left an empty water bottle in the car on a hot day. When she opened the door of her car at night, she felt the air in the car was cold and found the bottle compressed, as shown in Figure.
    Charles’ law
  2. Charles’ law gives the relationship between the volume and the temperature of a fixed mass of gas at constant pressure.
  3. The relationship between the volume and the temperature can be explained using the kinetic theory of gases.
    (a) When a gas in a closed container is heated, the average kinetic energy of the molecules increases. The temperature of the gas increases.
    (b) The rate of collision between the molecules and the walls of the container will increase if the volume is constant.
    (c) If the gas is allowed to expand, the faster molecules now move in a bigger space.
    (d) Therefore, the rate of collision between the molecules and the walls remains constant and thus, the pressure is constant.
    (e) For a gas which is heated, to remain at constant pressure, the gas must be allowed to expand and increase its volume.
  4. Charles’ law states that for a fixed mass of gas, the volume of the gas is directly proportional to its absolute temperature when its pressure is kept constant.
  5. The mathematical expression for Charles’ law:
    Charles’ law 5
  6. Consider a gas with an initial volume, V1 and temperature, T1. When the temperature changes to T2, the volume of the gas changes to V2.
    According to Charles’ law:
    Charles’ law 6
  7. The relationship between the volume and the absolute temperature of a gas under constant pressure can also be expressed with the graphs in Figure.
    Charles’ law 7

People also ask
What is the Boyle’s law?
What is the Pressure Law?

Experiment:

Aim: To determine the relationship between the volume and the temperature of a fixed mass of gas at constant pressure.
Problem: What is the relationship between the volume and the temperature of a fixed mass of gas at constant pressure?
Inference: The temperature of a gas affects its volume.
Hypothesis: The volume of a fixed mass of gas increases when the temperature is increased if the pressure is kept constant.
Variables:
(a) Manipulated variable: Temperature
(b) Responding variable: The volume of the air
(c) Fixed variables: The mass of the air in the capillary tube and the pressure
Operational Definition:
(a) The thermometer measures the temperature of the water. Since the water and the air in the capillary tube are in thermal equilibrium, the reading of the thermometer is defined operationally as the temperature of the air in the capillary tube.
(b) The volume of the air in the capillary tube is directly proportional to the length of the air column as the cross-sectional area of the tube is uniform. Therefore, the length of the air column is defined operationally to represent the volume of the air.
Materials: Concentrated sulphuric acid, some rubber bands
Apparatus: Capillary tube, thermometer, 600 ml beaker, wooden ruler, stirrer, tripod stand with wire gauze, Bunsen burner, retort stand with clamp
Method:
Charles’ law 1

  1. The apparatus is set up as shown in Figure.
  2. The water in the beaker is heated slowly and stirred continuously.
  3. When the temperature, θ = 30°C, the length of the air column, l is read on the ruler scale.
  4. Steps 2 and 3 are repeated for values of temperature, θ = 40°C, 50°C, 60°C, 70°C, 80°C and 90°C.
  5. The readings are tabulated. A graph of length of air column, l against temperature, θ is plotted.

Results:

  1. Tabulation of results.
    Charles’ law 2
  2. Graph of length of air column, l against temperature θ,
    Charles’ law 3

Discussion:

  1. The water was stirred continuously so that its temperature remained uniform.
  2. The graph of the length of the air column, l against the temperature, θ in °C is a straight line which does not pass through the origin. At 0°C, the molecules are still moving randomly and the air has a certain volume.
  3. When the straight line is extrapolated, it is found that the volume is expected to become zero at -273°C or the absolute zero of temperature.
  4. A graph of the length of the air column, l against absolute temperature, T is a straight line passing through the origin as shown in Figure.
    Charles’ law 4

Conclusion:
The volume of the gas is directly proportional to its absolute temperature. The hypothesis is accepted.

Charles’ Law Example Problems with Solutions

Example 1. Figure (a) shows an enclosed plastic bag containing 3.0 cm3 of air at a temperature of 2.0°C in a refrigerator. When the plastic bag was taken out and placed in a room where the temperature was 27.0°C, ) the air in it expanded, as shown in Figure (b).
Charles’ law 8
Calculate the final volume of the air in the plastic bag.
Solution:
Charles’ law 9

Example 2. Figure shows air trapped in an overturned empty crate floating on the sea. The volume of the air is 160 cm3 when the temperature of the sea water is 35.0°C.
Charles’ law 11
What is the temperature of the sea water, when the volume of the trapped air is 150 cm3?
Solution:
Charles’ law 10

 

What does Boyle’s Law state?

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What does Boyle’s Law state?

 

  1. Figure shows an air pillow. When the boy puts his head on the pillow, the air in the pillow is compressed. The pressure of the air increases to support his head.
    What does Boyle's Law state
  2. Boyle’s law gives the relationship between the pressure and the volume of a fixed mass of gas at constant temperature.
  3. The relationship between the pressure and the volume of a gas can be explained using the kinetic theory of gases.
    What does Boyle's Law state 1(a) When the volume of a gas is decreased, the number of molecules per unit volume increases.
    (b) The same number of molecules move in a smaller space as shown in Figure.
    (c) The molecules collide more frequently with the walls of the container.
    (d) The increase in the rate of collision results in an increase in the pressure exerted by the gas.
  4. Boyle’s law states that for a fixed mass of gas, the pressure of the gas is inversely proportional to its volume when the temperature is kept constant.
  5. The mathematical expression for Boyle’s law:
    What does Boyle's Law state 2that is, PV = constant when the temperature is kept constant.
  6. When the pressure changes from P1 to P2 the volume changes from V1 to V2.
    What does Boyle's Law state 3The product of pressure and volume remains constant. Therefore, P1V1 = P2V2.
  7. The equation for Boyle’s law is:
    What does Boyle's Law state 4when temperature and mass are constant.
    P1 = intial pressure P2 = final pressure
    V1 = initial volume V2 = final volume
  8. The relationship between the pressure and the volume can also be expressed with the graphs in Figure.
    What does Boyle's Law state 5

People also ask
What is the Charles Law?
What is the Pressure Law?

Experiment:

Inference: The pressure on a gas affects its volume.
Aim: To determine the relationship between the pressure and the volume of a fixed mass of gas at constant temperature.
Problem: What is the relationship between the pressure and the volume of a fixed mass of gas at constant temperature?
Hypothesis: The volume of a fixed mass of gas decreases when the pressure is increased.
Variables:
(a) Manipulated variable: Pressure
(b) Responding variable: Volume of the air
(c) Fixed variables: The mass of the air in the syringe and the temperature
Apparatus: A set of Boyle’s law apparatus consisting of a graduated glass syringe, standard weights, Bourdon gauge, rubber tubing, retort stand
Method:
What does Boyle's Law state 6

  1. The apparatus is set up as shown in Figure.
  2. The piston is pushed down until the Bourdon gauge shows a pressure, P = 110 kPa.
    The volume, V, of the air in the syringe is recorded.
  3. Steps 2 and 3 are repeated with pressures, P = 120 kPa, 130 kPa, 140 kPa and 150 kPa.
  4. The values of pressure, P, volume, V, 1/V and PV are tabulated.
  5. Graphs of P against V and P against 1/V are plotted.

Results:

  1. Tabulation of results.
    What does Boyle's Law state 7
  2. Graphs of P against V and P against 1/V.
    What does Boyle's Law state 8

Discussion:

  1. Some grease is applied on the piston so that it can move smoothly into the glass syringe.
  2. The piston moves slowly into the syringe after a standard weight is added. This ensures that the temperature of the air in the syringe remains constant.
  3. The graph of P against V shows that the volume of the gas decreases when its pressure is increased.
  4. The graph of P against 1/V is a straight line passing through the origin. This shows that P ∝ 1/V, that is, the pressure is inversely proportional to the volume.
  5. The product, PV, is said to be constant within the limits of experimental errors. This also shows that the pressure is inversely proportional to the volume.

Conclusion:
The volume of the air in the glass syringe is inversely proportional to the pressure. The hypothesis is accepted.

Boyle’s Law Example Problems with Solutions

Example 1. The air in a syringe has an initial volume of 12.0 cm3 and pressure of 100 kPa. The nozzle of the syringe is closed and the piston is pushed inwards until the volume of the air becomes 7.5 cm3. What is the pressure of the compressed air in the syringe?
Solution:
What does Boyle's Law state 9

Example 2. A deep-sea diver breathed out a bubble of air with a volume of 2.0 cm3 at a depth of 40 m. What will be the volume of the bubble when it is 15 m below the surface of the sea?
[Atmospheric pressure = 10 m of water]
Solution:
What does Boyle's Law state 10

Example 3. Figure shows a thin glass tube with air trapped inside it in three different positions.
What does Boyle's Law state 11
Determine the values of x and y.
[Atmospheric pressure = 76 cm Hg]
Solution:
What does Boyle's Law state 12