Question

A monoatomic ideal gas is used in a carnot engine as the working substance. If during the adiabatic compression the volume of the gas decreases from v to $\frac{v}{8}$, the efficiency of the engine is

• A. 0.5
• B. 0.25
• C. 0.75
• D. 0.4

Answer 1

The correct option is C 0.75

Let the temperature of the gas increases from $T_1$ and $T_2$ during adiabatic compression
$T_1{V}_1^{r-1}=T_2{V}_2^{r-1}$
$\Rightarrow \frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{r-1}=(8{)}^{\frac{2}{3}}=4$
Efficency $\eta =1-\frac{T_1}{T_2}=1-\frac{1}{4}=0.75$