A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then
- Compressing the gas isothermally or adiabatically will require the same amount of work.
- Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.
- Compressing the gas isothermally will require more work to be done.
- Compressing the gas through adiabatic process will require more work to be done.
Answer
(4) Compressing the gas through adiabatic process will require more work to be done.
Solution
Work done on the gas = area under the P–V curve between V and V2.
Starting from the same state, during compression the adiabatic curve is steeper than the isothermal curve (PV = constant vs PV = constant, > 1).
⇒ At every intermediate volume, Padiabatic > Pisothermal (the gas also heats up in adiabatic compression)
⇒ Area under the adiabatic curve is larger
∴ Adiabatic compression requires more work, whatever the atomicity of the gas.
Answer: (4)