First slide

First law of thermodynamics

Question

An ideal monoatomic gas is allowed to expand from state point A to state point B according to the process AB. Then heat supplied to the gas is

Moderate

A

$\frac{P_{0} V_{0}}{3}$
B

$\frac{3 P_{0} V_{0}}{4}$
C

$\frac{P_{0} V_{0}}{4}$
D

$\frac{1}{2} P_{0} V_{0}$

Solution

At A temperature is $T_{0}$
$∴ \frac{\frac{P_{0}}{2} . 2 V_{0}}{T_{B}} = \frac{P_{0} V_{0}}{T_{0}} \Rightarrow T_{B} = T_{0}$
$∴ ΔU =$ Change to internal energy $= n . C_{v} (T_{0} - T_{0}) = 0$
W = Work done by the gas $= \frac{1}{2} (P_{0} + \frac{P_{0}}{2}) . (2 V_{0} - V_{0}) = \frac{3 P_{0} V_{0}}{4}$
$∴ Heat supplied = ΔU + W = \frac{3 P_{0} V_{0}}{4}$

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