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Question
Can a process on an ideal gas be both adiabatic and isothermal?
Solution
According to the first law of thermodynamics, change in internal energy, ΔU is equal to the difference between heat supplied to the gas, Δ Q and the work done on the gas, ΔW,
such that ΔQ = ΔU +ΔW . In an adiabatic process, ΔQ =0 and in an isothermal process, change in temperature, Δ T =0. Therefore,
ΔQ = ΔU + ΔW
⇒ ΔQ = nCvΔT +ΔW
⇒ 0 =nCv(0) + Δ W
⇒ Δ W = 0 ,
if the process is adiabatic as well as isothermal, no work will be done. So, a process on an ideal gas cannot be both adiabatic and isothermal.
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