Is it possible to have an adiabatic process with a temperature change? why or why not? give two examples?

we have to consider first law of thermodynamics for an ideal gas

Answer:
Absolutely. The first law of thermodynamics is represented by the equation U= Q - W
Where W is the work done by the gas and Q is the heat transfer.
An adiabatic process is one that occurs so fast that there is no time for energy gain or loss from the external environment, such that Q = 0.
However U = mC(v) (delta T) and if W is not zero (i.e. the gas does work or has work done on it) then T final and T initial must be different values such that U is non zero and equal to W.
Thus adiabatic expansion and adiabatic compression are both examples of adiabatic process in which temperature changes (both are present in the carnot cycle, a cycle utilised by Carnot engines). This is also used in refrigerators and air conditioners.

Hope this helps.

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