First slide

Change in internal energy

Question

The internal energy of a gas is given by U = 2pV. It expands from V₀ to 2V₀ against a constant pressure $ρ_{0}$ . The heat absorbed by the gas in the process is

Moderate

A

$2 p_{0} V_{0}$
B

$4 p_{0} V_{0}$
C

$3 p_{0} V_{0}$
D

$p_{0} V_{0}$

Solution

Heat absorbed, $Q = W + Δ U$
$= p_{0} (2 V_{0} - V_{0}) + (2 p_{0} \cdot 2 V_{0} - 2 p_{0} V_{0})$
$= p_{0} V_{0} + 2 p_{0} V_{0} = 3 p_{0} V_{0}$

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