A diatomic gas $(\gamma=1.4)$ does $100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the…

A diatomic gas $(\gamma=1.4)$ does $100 \mathrm{~J}$ of work in an isobaric expansion. The heat given to the gas is :
  1. $250 \mathrm{~J}$
  2. $150 \mathrm{~J}$
  3. $350 \mathrm{~J}$
  4. $490 \mathrm{~J}$

Solution

For Isobaric process $\begin{aligned} & \mathrm{w}=\mathrm{P} \Delta \mathrm{v}=\mathrm{nR} \Delta \mathrm{T}=100 \mathrm{~J} \\ & \mathrm{Q}=\Delta \mathrm{u}+\mathrm{w} \\ & \Delta \mathrm{Q}=\frac{\mathrm{F}}{2} \mathrm{nR} \Delta \mathrm{T}+\mathrm{nR} \Delta \mathrm{T} \\ & \left(\frac{\mathrm{f}}{2}+1\right) \mathrm{nR} \Delta \mathrm{T} \\ & \left(\frac{5}{2}+1\right) 100=350 \mathrm{~J}\end{aligned}$
SECTION - B

Asked in: JEE Main 2024 (08 Apr Shift 2)

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