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Question
Can a process on an ideal gas be both adiabatic and isothermal?
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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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