JEE MAIN - Physics (2022 - 28th June Morning Shift - No. 7)
Given below are two statements :
Statement I : When $$\mu$$ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is $$W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}$$, where $$\gamma = {{{C_p}} \over {{C_v}}}$$ and R = universal gas constant.
Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below :
Explanation
$$W = {{\mu R({T_2} - {T_1})} \over {1 - r}}$$ for a polytropic process for adiabatic process r = $$\gamma$$
$$\Rightarrow$$ Statement I is true.
In an adiabatic process
$$\Delta$$U = $$-$$ $$\Delta$$W
$$\Rightarrow$$ If work is done on the gas
$$\Rightarrow$$ $$\Delta$$W is negative
$$\Rightarrow$$ $$\Delta$$U is positive or temperature increases
$$\Rightarrow$$ Statement II is true
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