Question

A sample consisting of 1 mole of a monoatomic perfect gas $\left(\begin{array}{c}{C}_v=\frac{3}{2}R\end{array}\right)$ is taken through the cycle as shown. $\Delta U$ for the process $(2⟶3)$ is :

• A. $0.00$ J
• B. $+3.40$ kJ
• C. $-3.40$ kJ
• D. None of the above

Answer 1

The correct option is C $-3.40$ kJ

In a conversion from state 2 to state 3,

$\Delta T=T_2-T_1$

$=273-546$
$=-273K$

$C_V=\frac{3}{2}R$

$\therefore$ $\Delta U=n{C}_V\Delta T$

$=1\times \frac{3}{2}\times 8.314\times (-273)$
$=-3.40\times {10}^{3}J$

$=-3.40\times KJ$

Therefore, option C is correct.