Question

Gaseous hydrogen contained initially under standard conditions in a sealed vessel of volume $V=5L$ was cooled by $\Delta T=55K$. The internal energy of the gas will change by

• A. $-255J$
• B. $200J$
• C. $250J$
• D. $-200J$

Answer 1

The correct option is A $-255J$

Volume of vessel $V=5L=0.005$ $m^3$

Standard conditions : $P=1$ atm $=1.01325\times {10}^5$ Pa $T=273.15K$

Using Ideal gas equation : $PV=nRT$

$\therefore$ $(1.01325\times {10}^5)\times 0.005=nR\times 273.15$ $⟹nR=1.8547$

Degree of freedom for diatomic gas $f=5$

Change in internal energy $\Delta U=\frac{f}{2}nR\Delta T=\frac{5}{2}\times 1.8547\times (-55)=-255$ $J$