Two moles of ideal helium gas are in a rubber | vedclass

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(D) For an ideal gas in a fully expandable balloon, the pressure $P$ remains constant because the balloon exerts no additional pressure during expansi

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$208$

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(D) For an ideal gas in a fully expandable balloon, the pressure $P$ remains constant because the balloon exerts no additional pressure during expansion.Thus, the process is isobaric.The heat required for an isobaric process is given by $\Delta Q = n C_p \Delta T$.For a monoatomic gas like helium, the degrees of freedom $f = 3$.The molar heat capacity at constant pressure is $C_p = \frac{f}{2} R + R = \frac{5}{2} R$.Given $n = 2$ moles, $\Delta T = 35^\circ C - 30^\circ C = 5 K$, and $R = 8.31$ $J/mol \cdot K$.$\Delta Q = n 	imes \frac{5}{2} R 	imes \Delta T = 2 	imes \frac{5}{2} 	imes 8.31 	imes 5$.$\Delta Q = 5 	imes 8.31 	imes 5 = 25 	imes 8.31 = 207.75 J \approx 208 J$.

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