Question

Two mole of ideal diatomic gas $(C_{v,m}=5/2R)$ at $300K$ and $10atm$ expanded irreversibly and adiabatically to a final pressure of $2atm$ against a constant pressure of 1 atm. Calculate change in internal energy $△U$

• A. $-2164.1J$
• B. $864.28J$
• C. $-1052.1J$
• D. $-1662.8J$

Answer 1

The correct option is D $-1662.8J$

For Adiabatic irreversible process
$n{C}_V(T_2-T_1)=-p_{ext}nR[\frac{T_2}{P_2}-\frac{T_1}{P_1}]$ .....eq (1)
Where, $C_v=\frac{5}{2}R$
$T_1=300K$
$P_{ext}=1atm,P_2=2atm$
$P_1=10atm$
$n=2$
so,
$2\times \frac{5}{2}R(T_2-300)=-2\times R[\frac{T_2}{2}-\frac{300}{10}]$

$5(T_2-300)=-2[\frac{T_2}{2}-\frac{300}{10}]$

Solving we get, $T_2=260K$
Now, From first law, $△U=q+w$
Since q =0,
$△w=△U=n{C}_v△T=2\times \frac{5}{2}\times 8.314\times (260-300)$ $=-1662.8J$