Question

Five moles of Hydrogen initially at STP is compressed adiabatically so that its temperature becomes $673K$. The increase in internal energy of the gas, in $kJ$ is:

[$R=8.3J/mole-K;\gamma =1.4$ for diatomic gas]

• A. $80.5$
• B. $21.55$
• C. $41.50$
• D. $65.55$

Answer 1

The correct option is C $41.50$

STP conditions : $T=273K$ $P=1atm$

Final temperature: $T^{\prime }=673K$

Number of moles of Hydrogen: $n=5$

Hydrogen is a diatomic gas, thus its degree of freedom: $f=5$

Increase in internal energy: $\Delta U=\frac{f}{2}nR\Delta T$

$\therefore$ $\Delta U=\frac{5}{2}\times 5\times 8.3\times (673-273)=41500J$

$⟹$ $\Delta U=41.5kJ$