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

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(D) Since the balloon is fully expandable and requires no energy for expansion,the pressure inside the balloon remains constant (equal to atmospheric

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$208$

Vedclass · Answer

(D) Since the balloon is fully expandable and requires no energy for expansion,the pressure inside the balloon remains constant (equal to atmospheric pressure). Thus,the process is isobaric.For an isobaric process,the heat required 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 $C_p = \frac{f}{2} R + R = \frac{3}{2} R + R = \frac{5}{2} R$.Given: $n = 2 \ mol$,$\Delta T = 35^{\circ} C - 30^{\circ} C = 5 \ K$,and $R = 8.31 \ J / mol \cdot K$.Substituting the values:$\Delta Q = 2 	imes \left( \frac{5}{2} 	imes 8.31 ight) 	imes 5$$\Delta Q = 5 	imes 8.31 	imes 5 = 25 	imes 8.31 = 207.75 \ J$.Rounding to the nearest integer,we get $\Delta Q \approx 208 \ J$.

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