Question

A sample consisting of 1mol 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 $(1⟶2)$ is :

• A. $0.00J$
• B. $3.40\times {10}^{3}J$
• C. $-3.40J$
• D. $-3.40\times {10}^{3}J$

Answer 1

Answer: (B)

$3.40\times {10}^{3}J$

in expansion from state 1 to state 2 :

$P=1atm$
$V_1=22.44L$
$V_2=44.88L$
$C_V=\frac{3}{2}R$

We know that,
$\Delta T=T_2-T_1$
$=546-273$
$=273K$

$\therefore$ $\Delta U=n{C}_V\Delta T$
$=1\times \frac{3}{2}\times 8.314\times 273$
$=3.40\times {10}^{3}J$