Level 1: A Gas Rushes Into a Vacuum: Does It Cool Down?
Make it push a piston instead.
An ideal monatomic gas (γ = 5/3) expands reversibly and adiabatically, pushing a piston, until its volume is doubled. Its absolute temperature falls to about:
In a reversible adiabatic expansion the gas does work on the piston with no heat coming in, so its internal energy and its temperature fall. Along such a process, the temperature times the volume raised to the power γ − 1 stays constant.
The temperature falls to about 0.63 of its starting value, because the gas paid for the work out of its own internal energy. In free expansion it paid nothing and stayed at T; 0.5 T would be right only if the temperature fell in proportion to the volume.
Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.
