**14 Boyle’s law Charles’s law Gay-Lussac’s law – Problems and Solutions**

1. The air pressure of car’s tire is 432 kPa with the temperature of 15 ^{o}C. After several hours, the pressure of air is 492 kPa. If expansion ignored, what is the temperature of air in the tire?

__Known :__

Initial pressure (P_{1}) = 432 kPa

Final pressure (P_{2}) = 492 kPa

Initial temperature (T_{1}) = 15 ^{o}C

__Wanted:__ Final temperature (T_{2})

__Solution :__

The equation of Gay-Lussac’s law :

2. Ideal gases in a closed container with volume V, pressure P, and temperature T. If its volume becomes ½ times the initial volume and its temperature becomes 4 times the initial temperature, what is the air pressure in the system.

__Known :__

The initial volume of gas (V_{1}) = V

The final volume of gas (V_{2}) = ½ V

The initial temperature of the gas (T_{1}) = T

The final temperature of the gas (T_{2}) = 4T

The initial pressure of the gas (P_{1}) = P_{1 }

__Wanted:__ the Final pressure of the gas (P_{2})

Solution :

3. Ideal gases initially in a container with volume V, temperature T, and pressure P. If gas heated so its temperature becomes 3/2 T and its pressure becomes 4/3 P, what is the volume of gas.

__Known :__

The initial volume of gas (V_{1}) = V

The initial temperature of the gas (T_{1}) = T

The final temperature of the gas (T_{2}) = 3/2 T

The initial pressure of the gas (P_{1}) = P

Final pressure of the gas (P_{2}) = 4/3 P

__Wanted:__ Final volume of gas (V_{2})

Solution :

4. Ideal gases initially in a container with volume V and pressure P. If the temperature of gas becomes 5/4 T and its volume becomes ¾ V, what is the final pressure of the gas.

__Known :__

The initial volume of gas (V_{1}) = V

The final volume of gas (V_{2}) = 3/4 V

The initial temperature of the gas (T_{1}) = T

The final temperature of the gas (T_{2}) = 5/4 T

The initial pressure of the gas (P_{1}) = P

__Wanted:__ the Final pressure of the gas (P_{2})

__Solution :__

5. Ideal gases initially in a container with volume V at temperature T and pressure P. If the temperature of gas becomes 3/2 T and its pressure becomes 2P, what is the final volume of gas.

__Known :__

The initial volume of gas (V_{1}) = V

The initial temperature of the gas (T_{1}) = T

The final temperature of the gas (T_{2}) = 3/2 T

The initial pressure of the gas (P_{1}) = P

Final pressure of the gas (P_{2}) = 2P

Wanted:__ Final volume of gas (V___{2})

__Solution :__

6. Ideal gases initially in a container with volume V at temperature T and pressure P. If the temperature of gas becomes 2T and pressure of gas becomes 3/2 P, what is the final volume of gas.

__Known :__

Initial volume (V_{1}) = V

Initial temperature (T_{1}) = T

Initial pressure (P_{1}) = P

Final temperature (T_{2}) = 2T

Final pressure (P_{2}) = 3/2 P

__Wanted:__ Final volume of gas (V_{2})

__Solution :__

7. The initial temperature of an ideal gas in a closed container is 27°C. If the final pressure is 4 times the initial pressure, what is the final temperature of the container?

Solution :

Closed container = constant volume = isochoric process

__Known :__

Initial temperature of gas (T_{1}) = 27^{o}C + 273 = 300 K

The initial pressure of the gas (P_{1}) = P

Final pressure of the gas (P_{2}) = 4P

__Wanted: __Final temperature of the gas (T_{2})

__Solution :__

8. In a closed container, the gas volume expands to 2 times the initial volume (V_{o} = initial volume, P_{o} = initial pressure) and the temperature of gas becomes 4 times the initial temperature. What is the final pressure of the gas?

__Known :__

The initial volume of gas (V_{1}) = V_{o}

The final volume of gas (V_{2}) = 2V_{o}

The initial temperature of the gas (T_{1}) = T

The final temperature of the gas (T_{2}) = 4T

The initial pressure of the gas (P_{1}) = P_{o }

__Wanted:__ the Final pressure of the gas (P_{2})

__Solution :__

9. An ideal gas in closed container initially at 27°C. If the final pressure is 4 times the initial pressure, what is the temperature of the container?

__Solution :__

Closed container = constant volume = isochoric process.

__Known :__

Initial temperature of gas (T_{1}) = 27^{o}C + 273 = 300 K

The initial pressure of the gas (P_{1}) = P

Final pressure of the gas (P_{2}) = 4P

__Wanted:__ Final temperature of the gas (T_{2})

__Solution :__

10. An ideal gas undergoes the isothermal process, so its pressure becomes 2 times the initial pressure. What is the final volume?

Isothermal = constant temperature

__Known :__

The initial volume of gas (V_{1}) = V

The initial pressure of the gas (P_{1}) = P

Final pressure of the gas (P_{2}) = 2P

__Wanted:__ Final volume of gas (V_{2})

__Solution :__

P_{1} V_{1} = P_{2} V_{2}

P V = (2P) V_{2}

V = (2) V_{2}

V_{2} = V / 2

V_{2} = ½ V

11. An ideal gas in a closed container with pressure P, volume V and temperature T. The final temperature is 2T and the final volume is 3/2 V. What is the ratio of the initial pressure (P_{1}) to the final pressure (P_{2}).

__Known :__

Initial pressure (P_{1}) = P

Initial volume (V_{1}) = V

Final volume (V_{2}) = 3/2 V

Initial temperature (T_{1}) = T

Final temperature (T_{2}) = 2T

__Wanted:__ The ratio of the initial pressure (P_{1}) to the final pressure (P_{2})

__Solution :__

The ratio of the initial pressure to the final pressure :

P_{1 }: P_{2}

P : 4P/3

1 : 4/3

3 (1) : (3) 4/3

3 : 4

12. Oxygen gas with volume V, temperature T and pressure P in a closed container. The final volume of the oxygen gas is 3/4 V and the final temperature is 3/2 T. What is the ratio of the initial pressure to the final pressure.

__Known :__

Initial pressure (P_{1}) = P

Initial volume (V_{1}) = V

Final volume (V_{2}) = 3/4 V

Initial temperature (T_{1}) = T

Final temperature (T_{2}) = 3/2 T

__Wanted:__ The ratio of the initial pressure (P_{1}) to the final pressure (P_{2})

__Solution :__

The ratio of the initial pressure to the final pressure :

P_{1 }: P_{2}

P : 2P

1 : 2

13. An ideal gas initially in a container with a volume of V, the temperature of T and pressure of P. If the ideal gas heated so its temperature becomes 3/2 T and its pressure becomes 4/3 P, then what is the final volume of the ideal gas.

__Known :__

Initial volume (V_{1}) = V

Initial temperature (T_{1}) = T

Initial pressure (P_{1}) = P

Final temperature (T_{2}) = 3/2 T

Final pressure (P_{2}) = 4/3 P

__Wanted:__ Final volume (V_{2})

__Solution :__

14. An ideal gas in a container with a volume of V_{1}, the temperature of T_{1 }and pressure of P_{1}. Then the gas heated so its volume becomes 4/3 V_{1} and its pressure become 5/2 P_{1}. Determine the comparison of the final temperature and the initial temperature of the gas.

__Known :__

Initial volume = V_{1}

Initial temperature = T_{1}

Initial pressure = P_{1}

Final volume = 4/3 V_{1}

Final pressure = 5/2 P_{1}

Wanted:__ the comparison of the final temperature and the initial temperature of the gas__

__Solution :__