Question
Air in a cylinder, is suddenly compressed to half of its initial volume by a piston which is then maintained at that new position. What happens to the pressure of gas with the passage of time?
Solution
Sudden compression is an adiabatic compression.
Thus, just after compression, the pressure of gas increases to 2γP which is greater than the initial pressure. The temperature increases to 2γ–1 T, which is greater than T.
Here,
P is the initial pressure, and
T is the initial temperature.
With the passage of time, the temperature of air starts decreasing due to loss of heat to the surrounding. This results in the decrease of pressure at constant volume. Finally the pressure of air decreases to 2P.
Thus, just after compression, the pressure of gas increases to 2γP which is greater than the initial pressure. The temperature increases to 2γ–1 T, which is greater than T.
Here,
P is the initial pressure, and
T is the initial temperature.
With the passage of time, the temperature of air starts decreasing due to loss of heat to the surrounding. This results in the decrease of pressure at constant volume. Finally the pressure of air decreases to 2P.
