Physics

Problem

A sample of ideal gas expands along a straight-line path on a

P

–

V

diagram from the initial state (

4\times10^5\,\text{Pa}

2.0\,\text{L}

) to the final state (

1\times10^5\,\text{Pa}

5.0\,\text{L}

). During this process,

800\,\text{J}

of heat is supplied to the gas. a. (i) Calculate the work done by the gas. b. (ii) Determine the change in internal energy of the gas.

Intuitive explanation

The key is recognizing that work done by the gas depends on the area under the curve on a $P$ – $V$ diagram, even though the path is a straight line. Since pressure and volume change together linearly, you'll need to find that area (a trapezoid), then use the first law of thermodynamics ( $\Delta U = Q - W$ ) to connect heat supplied, work done, and the change in internal energy. This tells you whether the gas heats up or cools down overall.

Intuitive explanation

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