Question

The efficiency of a carnot cycle on a monoatomic gas is $50$ %. The lowest temperature during the cycle is ${27}^{\circ }C$. If there are $3moles$ of gas, what is the change in its internal energy during adiabatic expansion of the cycle?
$[R=8.3J/mol-K]$.

• A. $101.25J$
• B. $-101.25J$
• C. $-11.2kJ$
• D. $11.2kJ$

Answer 1

The correct option is C $-11.2kJ$

Efficiency of carnot cycle $\eta =1-\frac{T_2}{T_1}\Rightarrow \frac{1}{2}=1-\frac{300}{T_1}\Rightarrow T_1=600K\Rightarrow \Delta T=300K$

Change in internal energy in an adiabatic process:
$\Delta U=\frac{nR\Delta T}{\gamma -1}=\frac{(3\times 8.3\times (300-600)}{\frac{5}{3}-1}\Delta U=-11.2kJ$