Question

Six moles of $O_2$ gas is heated from $20^{\circ }C$ to $35^{\circ }C$ at constant volume. If specific heat capacity at constant pressure is $8cal/mol-K$ and $R=8.31J/mol-K$ what is change in internal energy of gas

• A. $180cal$
• B. $300cal$
• C. $360cal$
• D. $540cal$

Answer 1

Answer: (D)

Consider $n$ moles of a gas which undergo isochoric process, i.e., $V=$ constant. From first law of thermodynamics,
$\Delta Q=\Delta W+\Delta U...(i)$
Here, $\Delta W=0$ as $V=$ constant
$\Delta Q={}^n{C}_V\Delta T$
Substituting in Eq.(i), we get
$\Delta U=n{C}_V\Delta T...(ii)$
Mayor’s relation can be written as
$C_P-C_V=R$
$\Rightarrow C_V=C_P-R...(iii)$
From Eqs.(ii) and (iii), we have
$\Delta U=n(C_P-R)\Delta T$
Given, $n=6,C_P=8cal/mol-K$,
$R=8.31J/mol-K$
$\approx 2cal/mol-K$
Hence, $\Delta U=6(8-2)(35-20)$
$=6\times 6\times 15=540cal$