Two identical Carnot (cycles) engines operate between maximum and...

Two identical Carnot (cycles) engines operate between maximum and minimum temperatures

\mathrm{T}_1

and

\mathrm{T}_2

and volume limits,

\mathrm{V}_2, \mathrm{~V}_{\mathrm{b}}, \mathrm{V}_{\mathrm{c}} \ \text{ and } \mathrm{~V}_{\mathrm{d}}

as shown in figure. Given that

\frac{\mathrm{V}_{\mathrm{c}}}{\mathrm{V}_{\mathrm{a}}}=\mathrm{e}^3

and

\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\mathrm{e}

(e is the base of natural logarithm). Engine 1 operates on mono atomic gas while the engine 2 on diatomic gas. Choose correct alternatives Two identical Carnot (cycles) engines operate between maximum and minimum temperatures T_1 and T_2 and volume limits,

Two identical Carnot (cycles) engines operate between maximum and minimum temperatures T_1 and T_2 and volume limits,

Options

ARatio of volumes $\frac{\mathrm{V}_{\mathrm{b}, 1}}{\mathrm{~V}_{\mathrm{b}, 2}}=\mathrm{e}$
BRatio of work done per cycle for the two is $\frac{W_1}{W_2}=3$
CRatio of work per cycle for the two is $\frac{W_1}{W_2}=1$
DRatio of efficiencies ( $\eta$ ) of two engines $\frac{\eta_1}{\eta_2}=1$

Correct answer

D. Ratio of efficiencies ( $\eta$ ) of two engines $\frac{\eta_1}{\eta_2}=1$

Step-by-step solution

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