In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A arrow B and C arrow D are T1 and T2(T1 T2) respectively. Choose the correct option out of the following for work done if processes B C and D A are adiabatic.

Question

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A arrow B and C arrow D are T1 and T2(T1 >T2) respectively.

Choose the correct option out of the following for work done if processes B C and D A are adiabatic. (A) WA B=WD C (B) WA D=WB C (C) WB C+WD A>0 (D) WA B < WC D

Tardigrade Admin · Accepted Answer

Work done in adiabatic process =(-n R/&gamma;-1)(Tf-Ti) ∴ WA D=(-n R/&gamma;-1)(T2-T1) and WB C=(-n R/&gamma;-1)(T2-T1) ∴ WA D=WB C

$W_{A B} = W_{D C}$

$W_{A D} = W_{BC}$

$W_{BC} + W_{D A} > 0$

$W_{A B} < W_{C D}$

Work done in adiabatic process $= \frac{- n R}{γ - 1} (T_{f} - T_{i})$
$∴ W_{A D} = \frac{- n R}{γ - 1} (T_{2} - T_{1})$
and $W_{BC} = \frac{- n R}{γ - 1} (T_{2} - T_{1})$
$∴ W_{A D} = W_{BC}$

WAB​=WDC​

WAD​=WBC​

WBC​+WDA​>0

WAB​<WCD​

Work done in adiabatic process =γ−1−nR​(Tf​−Ti​) ∴WAD​=γ−1−nR​(T2​−T1​) and WBC​=γ−1−nR​(T2​−T1​) ∴WAD​=WBC​

$W_{A B} = W_{D C}$

$W_{A D} = W_{BC}$

$W_{BC} + W_{D A} > 0$

$W_{A B} < W_{C D}$

Work done in adiabatic process $= \frac{- n R}{γ - 1} (T_{f} - T_{i})$
$∴ W_{A D} = \frac{- n R}{γ - 1} (T_{2} - T_{1})$
and $W_{BC} = \frac{- n R}{γ - 1} (T_{2} - T_{1})$
$∴ W_{A D} = W_{BC}$