A graph drawn between absolute temperature and volume of 3 moles of...

A graph drawn between absolute temperature and volume of 3 moles of helium gas as shown in the figure. If

5 \mathrm{cal}

of heat is used in the process, then the work done is A graph drawn between absolute temperature and volume of 3 moles of helium gas as shown in the figure. If 5 cal of heat

A graph drawn between absolute temperature and volume of 3 moles of helium gas as shown in the figure. If 5 cal of heat

Options

A21.0 J
B8.4 J
C12.6 J
D6.2 J

Correct answer

B. 8.4 J

Step-by-step solution

In given graph, V \propto T \Rightarrow

\frac{V}{T}=\text{ constant }

Hence, process is a constant pressure process.

\text{ So, }

\begin{aligned} \DeltaQ= & n C_p \DeltaT \text{ and } \DeltaW=p \DeltaV=n R \DeltaT=n R \cdot \frac{\Delta Q}{n C_p}\\ = & \frac{\Delta Q R}{\frac{5}{2} R}=\frac{2}{5} \times \DeltaQ=2 \mathrm{cal}=2 \times4.2 \mathrm{~J}=8.4 \mathrm{~J} \end{aligned}

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