Question

In an adiabatic compression, a gas's temperature (a) increases; (b) decreases; (c) remains the same; (d) cannot be determined from the information given.

Solution

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Writing down the first law we get:

ΔU=W+Q\begin{align*} \Delta U & = W + Q \end{align*}

Because this is an adiabatic process, Q=0Q = 0. Because the gas is compressed, the work is done on it, W>0W > 0. Putting all this together we get:

ΔU=W>0\begin{align*} \Delta U & = W > 0 \end{align*}

Because the internal energy of an ideal gas is only a function of temperature, the temperature of the gas will increase.

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