Two moles of ideal helium gas are in a rubber balloon at $30^{\circ} \mathrm{C}$. The balloon is fully…
Two moles of ideal helium gas are in a rubber balloon at $30^{\circ} \mathrm{C}$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^{\circ} \mathrm{C}$. The amount of heat required in raising the temperature is nearly (take $R=8.31 \mathrm{~J} / \mathrm{mol} . \mathrm{K}$ )
$62 \mathrm{~J}$
$104 \mathrm{~J}$
$124 \mathrm{~J}$
$208 \mathrm{~J}$
Solution
The heat is supplied at constant pressure. i.e., the process is isobaric
$\begin{array}{l}
\therefore Q=n C_{p} \Delta t \\
=2\left[\frac{5}{2} R\right] \times \Delta t=2 \times \frac{5}{2} \times 8.31 \times 5=208 \mathrm{~J} \\
\left(\because C_{p}=\frac{5}{2} R \text { for mono-atomic gas }\right)
\end{array}$