Question

Inside a rubber balloon, two moles of helium molecules are present at $30{}^\circ C$. The balloon is fully expandable and we can assume that there is no requirement of energy in its expansion. The temperature of the gas in the balloon is slowly varied to $35{}^\circ C$. The amount of heat needed in raising the temperature will be approximately (take $R=8.31J/molK$)
$\begin{aligned} & A.62J \\\ & B.104J \\\ & C.124J \\\ & D.208J \\\ \end{aligned}$

Answer 1

The pressure inside the balloon is a constant. Therefore the process will be an isobaric process. The change in heat energy will be equivalent to the product of the number of moles, specific heat capacity at constant pressure and the change in temperature. Substitute the values in it. These details will help you in solving this question.

Complete answer:
Here when we examine the question, we can see that the pressure inside the balloon will be a constant. Hence the process can be considered as an isobaric process. At constant pressure, the change in heat energy will be equivalent to the product of the number of moles, specific heat capacity at constant pressure and the change in temperature.
This can be written as an equation,
$\Delta Q=n{{C}_{P}}\Delta T$
It is already given in the question that the number of moles of helium gas inside the balloon will be,
$n=2$
The helium gas is a monatomic molecule therefore the value of specific heat capacity at constant volume will be,
${{C}_{P}}=\dfrac{5}{2}R$
The change in temperature can be expressed as,
$\Delta T=35-30=5{}^\circ C$
In kelvin also the change in temperature will be the same. That is,
$\Delta T=5K$
Substituting the values in it will give,
$\Delta Q=2\times \dfrac{5}{2}R\times 5=25R$
Here the value of universal constant is mentioned as,
$R=8.31J/molK$
Substituting this in the equation,
$\Delta Q=25R=25\times 8.31=207.75\approx 208J$

The answer is given as option D.

Note:
Specific heat at constant pressure is defined as the ratio of the amount of heat required to raise the temperature of a unit mass of particles by a unit degree to the amount of heat required to raise that of the identical mass of water by the equal amount at constant pressure. Specific heat at constant volume is defined as the same. The only difference is that the volume will be constant here, not the pressure.