Practice It

Use the worked example above to help you solve this problem. In a car engine operating at $1\mathrm{.}85{10}^{-1}re\frac{v}{m}in,$ the expansion of hot, high$-$pressure gas against a piston occurs in about $10$ ms $.$ Because energy transfer by heat typically takes a time on the order of minutes or hours, it's safe to assume that little energy leaves the hot gas during the expansion.

Estimate the work done by the gas on the piston during this adiabatic expansion by assuming the engine cylinder contains $0\mathrm{.}185$ moles of an ideal monatomic gas which goes from $1\mathrm{.}20{10}^{3}K$ to $4\mathrm{.}00{10}^{2}K,$ typical engine temperatures, during the expansion.

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Exercise

A monatomic ideal gas with volume $0\mathrm{.}185$ L is rapidly compressed, so the process can be considered adiabatic. If the gas is initially at $1\mathrm{.}01{10}^{5}Pa$ and $3\mathrm{.}00{10}^{2}K$ and the final temperature is $463$ K $,$ find the work done by the gas on the efivironment, $w_{\text{e}\text{n}\text{v}}.$

$w_{\text{e}\text{n}\text{v}}$