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Thermodynamic Processes

A container h...

Question

A container having slightly conducting walls contains air. The initial temperature and volume are $47^{o} C$ (equal to the temperature of the surrounding) and $400 c m^{3}$ respectively. Find the rise in temperature if the gas is compressed to $200 c m^{3}$ in a very short time. Take $γ = 1.4 [2^{0.4} = 1.3]$

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Solution

When the gas is compressed in a short time, the process is adiabatic. Thus,
$T_{2} V_{2}^{γ - 1} = T_{1} V_{2}^{γ - 1}$
or $T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ - 1} = (320 K) \times {[\frac{400}{200}]}^{0.4} = 416 K$
Rise in temperature $= T_{2} - T_{1} = 96 K$ .

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