Question

$1$ mol of an ideal gas for which $C_v=\frac{3}{2}R$ is heated reversibly at a constant pressure of $1$ atm from $25{}^{o}C$ to $100{}^{o}C$. The $△H$ is:
Given: $R=1.987\text{cal}$

• A. $3.775\text{cal}$
• B. $37.256\text{cal}$
• C. $372.56\text{cal}$
• D. $3725.6\text{cal}$

Answer 1

The correct option is C $372.56\text{cal}$

We know that,
$△H$ = $△U$ + P$△V$
Given number of moles $n=1,$
So, $PV=RT$, P$△V=$ R$△T$
We also know,
$△U=$ $C_v\times (T_2-T_1)$ for 1 mole of a gas.
Put up value of $\Delta U$ in formula,
$=(\frac{3}{2}\times R\times 75)$ + $(R\times 75)$
$=\frac{5}{2}\times R\times 75$
$=372.56\text{cal}$ $(R=1.987\text{cal})$