A polyatomic gas with six degrees of freedom does 25,,J of work when it is expanded at constant pres

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11.Thermodynamics

hard

A polyatomic gas with six degrees of freedom does $25\,\,J$ of work when it is expanded at constant pressure. The heat given to the gas is ..... $J$

A

$100$

B

$150$

C

$200$

D

$250$

Solution

freedom $(f)=6^{0}$

$r=1+\frac{2}{6}=\frac{4}{3}$

$\frac{\Delta w}{\Delta Q}=\frac{\Delta Q-\Delta u}{\Delta Q}=1-\frac{\Delta u}{\Delta Q}=1-\frac{n c u \Delta T}{n c p \Delta T}$

$\Rightarrow 1-\frac{1}{r}=1-\frac{1}{\frac{4}{3}}=\frac{4-3}{4}=\frac{1}{4}$

$\Rightarrow \frac{\Delta w}{\Delta Q}=\frac{1}{4}$

$\therefore \quad \Delta Q=4 \times \Delta w=4 \times 25 j=100 j$

Standard 11

Physics

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