Calculate the change in internal energy of a gas kept in a rigid container when $100 J$ of heat is supplied to it.

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Solution

Given data,
Heat supplied to the system
$Δ Q = 100 J$
Using the first law of thermodynamics, we get
$Δ U = Δ Q - Δ W$
Since the container is rigid, initial volume of the system is equal to the final volume of the system. Thus,
$Δ V = V_{f} - V_{i} = 0$
$Δ W = P$
$Δ V = 0$
$Δ U = Δ Q = 100 J$
We see that heat supplied to the system is used up in raising the internal energy of the system.

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