1. Ideal gases initially have pressure P and temperature T. The gas undergoes the isochoric process so that the final pressure becomes 4 times the initial pressure. What is the final temperature of the gas?
Known :
Initial pressure (P1) = P
Final pressure (P2) = 4P
Initial temperature (T1) = T
Wanted: Final temperature (T2)
Solution :
The formula of Gay-Lussac’s law :
The final temperature becomes 4 times the initial temperature.
2. In a closed container, ideal gases initially have a temperature of 27oC. If the final pressure becomes 2 times the initial pressure, what is the final temperature?
Known :
Initial pressure (P1) = P
Final pressure (P2) = 2P
Initial temperature (T1) = 27oC + 273 = 300 K
Wanted: Final temperature (T2)
Solution :
3. A tire is filled to a gauge pressure of 2 atm at 27°C. After a drive, the temperature within the tire rises to 47°C. What is the pressure within the tire now?
Known :
The atmospheric pressure = 1 atm = 1 x 105 Pa
The initial gauge pressure = 2 atm = 2 x 105 Pa
The initial absolute pressure (P1) = 1 atm + 2 atm = 3 atm = 3 x 105 Pa
The initial temperature (T1) = 27oC + 273 = 300 K
The final temperature (T1) = 47oC + 273 = 320 K
Wanted : The final gauge temperature
Solution :
The final gauge pressure = final absolute pressure – atmospheric pressure
The final gauge pressure = 3.2 atm – 1 atm
The final gauge pressure = 2.2 atm
