Question

Gaseous hydrogen contained initially under standard conditions in a sealed vessel of volume $V=5L$ was cooled by $\Delta T=55K$. What amount of heat will be lost by the gas (in Joules) ?

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

Answer 1

The correct option is A $-255$

By the first law of thermodynamics
$\Delta Q=\Delta U+\Delta W$
Here $\Delta W=0$ as the volume remains constant.
$\therefore \Delta Q=\Delta U$
Now $\Delta U=n{C}_v(-\Delta T)$
$=-n\frac{R}{\gamma -1}\Delta T$ $(as{C}_v=\frac{R}{\gamma -1})$
We have $P_{o}V=nR{T}_0$
or
$nR=\frac{P_{o}V}{T_o}$
Thus we get
$\Delta U=-\frac{1.013\times {10}^5\times (5\times {10}^{-3})\times 55}{273(1.4-1)}=-255J$