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Molar and Specific Heat Capacity

In the figure...

Question

In the figure, an ideal gas changes its state from state $A$ to state $C$ by two paths $A B C$ and $A C$ .
The internal energy of gas in state $B$ is $60 J$ . Find the amount of heat supplied to the gas to go from $A$ to $B$ .

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Solution

Path $A$ to $B$
$U_{B} = 60 J ∴ △ U = Q - W_{A B}$
$U_{B} - U_{A} = Q - 0; 60 - 30 = Q$
$∴ Q = 30 J$ .

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