Two moles of ideal helium gas are in a rubber balloon at 30^ C ....

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}

)

Options

A $62 \mathrm{~J}$
B $104 \mathrm{~J}$
C $124 \mathrm{~J}$
D $208 \mathrm{~J}$

Correct answer

D. $208 \mathrm{~J}$

Step-by-step 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}

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