A diatomic ideal gas is used in a Carnot engi | vedclass

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(C) For a diatomic gas,the adiabatic index $\gamma = 1.4 = 7/5$.In an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamm

Vedclass · Accepted Answer

$0.75$

Vedclass · Answer

(C) For a diatomic gas,the adiabatic index $\gamma = 1.4 = 7/5$.In an adiabatic process,the relation between temperature and volume is $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Given $V_1 = V$ and $V_2 = 32V$,we have:$T_1 (V)^{7/5 - 1} = T_2 (32V)^{7/5 - 1}$$T_1 (V)^{2/5} = T_2 (32V)^{2/5}$$T_1 = T_2 (32)^{2/5}$$T_1 = T_2 (2^5)^{2/5} = T_2 (2^2) = 4T_2$.The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$.Substituting $T_1 = 4T_2$:$\eta = 1 - \frac{T_2}{4T_2} = 1 - 0.25 = 0.75$.

$A$ diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

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