1. Some ideal gases initially have pressure P and volume V. If the gas undergoes isothermal process so that the final pressure becomes 4 times the initial pressure, then the final volume of gas is…
Known :
Initial pressure (P1) = P
Final pressure (P2) = 4P
Initial volume (V1) = V
Wanted: Final volume (V2)
Solution :
The formula of Boyle’s law :
P V = constant
P1 V1 = P2 V2
(P)(V) = (4P)(V2)
V = 4 V2
V2 = V / 4 = ¼ V
The final volume of gases is ¼ times the initial volume.
2. In a closed container, the gas expands so that the final volume becomes 2 times the initial volume (V = initial volume, P = initial pressure). The final pressure of gases is…
Known :
Initial pressure (P1) = P
Initial volume (V1) = V
Final volume (V2) = 2V
Wanted : Final pressure (P2)
Solution :
P1 V1 = P2 V2
P V = P2 (2V)
P = P2 (2)
P2 = P / 2 = ½ P
The gases pressure becomes ½ times the initial pressure.
3. In a closed container, gases having a pressure of 2 atm and a volume of 1 liter. If gas pressure becomes 4 atm then gas volume becomes …
Known :
Initial pressure (P1) = 2 atm = 2 x 105 Pa
Final pressure (P2) = 4 atm = 4 x 105 Pa
Initial volume (V1) = 1 liter = 1 dm3 = 1 x 10-3 m3
Wanted : Final volume (V2)
Solution :
P1 V1 = P2 V2
(2 x 105)(1 x 10-3) = (4 x 105) V2
(1)(1 x 10-3) = (2) V2
1 x 10-3 = (2) V2
V2 = ½ x 10-3
V2 = 0.5 x 10-3 m3 = 0.5 dm3 = 0.5 liters
