In an adiabatic expansion of a gas initial and final temperatures are $T_1$ and $T_2$ respectively then the…

In an adiabatic expansion of a gas initial and final temperatures are $T_1$ and $T_2$ respectively then the change in internal energy of the gas is $\text {[R = gas constant, } \gamma=\text { adiabatic ratio }]$
  1. zero
  2. $\frac{n R}{\gamma-1}\left(T_1-T_2\right)$
  3. $\frac{\mathrm{nR}}{\gamma-1}\left(\mathrm{~T}_2-\mathrm{T}_1\right)$
  4. $\mathrm{nR}\left(\mathrm{T}_1-\mathrm{T}_2\right)$

Solution

The correct option is (C). Concept: In adiabatic process work done is equal to change in internal energy as there is not enough time for heat transfer. $\Delta \mathrm{W}=\Delta \mathrm{U}$ Work done can be calculated by relation: $\Delta \mathrm{W}=-\int \mathrm{p} \mathrm{dV}$.

Asked in: MHT CET 2022 (05 Aug Shift 1)

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