A Carnot heat engine works with an ideal diat | vedclass

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Question

(B) For a diatomic gas, the adiabatic index $\gamma = 1.4 = 7/5$. The adiabatic expansion process is given by $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(B) For a diatomic gas, the adiabatic index $\gamma = 1.4 = 7/5$. The adiabatic expansion process is given by $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Given the expansion ratio $V_2/V_1 = 32$, we have $T_1/T_2 = (V_2/V_1)^{\gamma-1}$.Substituting the values: $T_1/T_2 = (32)^{7/5 - 1} = (32)^{2/5}$.Since $32 = 2^5$, we get $T_1/T_2 = (2^5)^{2/5} = 2^2 = 4$.The efficiency of a Carnot engine is given by $\eta = (1 - T_2/T_1) 	imes 100 \%$.Substituting $T_2/T_1 = 1/4$, we get $\eta = (1 - 1/4) 	imes 100 \% = (3/4) 	imes 100 \% = 75 \%$.

$A$ Carnot heat engine works with an ideal diatomic gas and an adiabatic volume expansion ratio of $32$. Then its efficiency is ....... $\%$

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