Air (γ = 1.40) at 1.0 × 10⁵ Pa and 290 K is squeezed quickly to 1/12 of its volume…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Air ( $\gamma = 1.40$ ) at $1.0 \times 10^{5}\ \text{Pa}$ and $290\ \text{K}$ is squeezed quickly to $\tfrac{1}{12}$ of its volume. Find its final temperature, in kelvin and in degrees Celsius, and its final pressure.

Need a reminder? The key ideaShow

Adiabatic: $Q = 0$ , so $W = -\Delta U = nC_v(T_1 - T_2) = \dfrac{p_1V_1 - p_2V_2}{\gamma - 1}$ . Along the way $pV^\gamma$ and $TV^{\gamma - 1}$ stay the same. Squeezed, the gas warms; expanding, it cools.

The worked solution

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Air (γ = 1.40) at 1.0 × 10⁵ Pa and 290 K is squeezed quickly to 1/12 of its volume…

The worked solution

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