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Question

The graph shows variation of internal energy $U$ with density $ρ$ of one mole of an ideal monatomic gas. The process $A B$ is a part of rectangular hyperbola. Find the work done (in $J$ ) in the process.

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Solution

For rectangular hyperbola,
$U_{ρ} = Constant$
$\frac{T}{V} = Constant$
$P = Constant$
So, the gas undergoes isobaric process
$W = n R Δ T ˙ . . . . (i)$
From graph, change in internal energy
$n (C_{v}) Δ T = 3$
$n (\frac{3 R}{2}) Δ T = 3$
$\Rightarrow n R Δ T = 3$
$\Rightarrow W = 2 J$
Final answer: $(2)$

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