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1.5 mol of an ideal gas expands slowly at a steady 320 K from 8.0 to 24 litres.

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

$1.5\ \text{mol}$ of an ideal gas expands slowly at a steady $320\ \text{K}$ from $8.0$ to $24$ litres. Find the work it does, its change of internal energy and the heat it takes in. What are its pressures at the start and the end? ( $R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}$ )

Need a reminder? The key ideaShow

Work done by a gas is the area under its path on a pressure-volume graph. At a steady pressure $W = p\,\Delta V$ ; along a straight line, the average pressure times $\Delta V$ ; at a steady temperature $W = nRT\ln\dfrac{V_2}{V_1}$ . Expanding gives positive work, squeezing negative. $1\ \text{L} = 10^{-3}\ \text{m}^3$ .

Isothermal: $\Delta U = 0$ , $Q = W = nRT\ln\dfrac{V_2}{V_1}$ . Isobaric: $W = p\,\Delta V = nR\,\Delta T$ , $Q = nC_p\,\Delta T$ . Isochoric: $W = 0$ , $Q = \Delta U = nC_v\,\Delta T$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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