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Standard XII

Physics

Heat Engines

An ideal diat...

Question

An ideal diatomic gas is enclosed in an insulated chamber at temperature $300 K$ . The chamber is closed by a freely movable massless piston, whose initial height from the base is $1 m$ . Now the gas is heated such that its temperature becomes $400 K$ at constant pressure. Find the new height of the piston from the base.
If the gas is compressed to initial position such that no exchange of heat takes place, find the final temperature of the gas.

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Solution

Process $1$ is isobaric
$T_{1} = 300 K, T_{2} = 400 K$
$\frac{V}{T} = c o n s t a n t$
$\frac{A \times 1}{300} = \frac{A \times h}{400} \Rightarrow h = \frac{4}{3} m$
Process $2$ is adiabatic
$T V^{r - 1} = c o n s t a n t$ ,
$400 {(\frac{A \times 4}{3})}^{\frac{7}{5} - 1} = T_{3} (A \times 1)^{\frac{7}{5} - 1}$
$\Rightarrow T_{3} = 400 {(\frac{4}{3})}^{\frac{2}{5}} K$ .

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Process 1 is isobaricT1=300 K,T2=400 KVT=constantA×1300=A×h400⇒h=43mProcess 2 is adiabaticTVr−1=constant,400(A×43)75−1=T3(A×1)75−1⇒T3=400(43)25K.