First slide

First law of thermodynamics

Question

Two mole of a diatomic ideal gas is taken through the process PT=constant. Its temperature is increased from $T_{0} K$ to $2 T_{0} K$ . Find work done by the system?
( R is gas constant)

Difficult

A

$6 R T_{0}$
B

$\frac{11}{2} R T_{0}$
C

$\frac{9}{2} R T_{0}$
D

$4 R T_{0}$

Solution

$\begin{array}{l} P T = c o n s t \\ \Rightarrow P . \frac{P V}{n R} = c o n s t \Rightarrow P V^{\frac{1}{2}} = c o n s t \end{array}$
It is a polytropic process with n=1/2
$H e n c e C = C_{v} + \frac{R}{1 - \frac{1}{2}} = \frac{5}{2} R + 2 R = 4.5 R$
$Δ Q = n C Δ T = 2 \times 4.5 R \times T_{0} = 9 R T_{0}$
$Δ U = n C_{v} Δ T = 2 \times 2.5 R \times T_{0} = 5 R T_{0}$
$Δ Q = Δ W + Δ U \Rightarrow Δ W = Δ Q - Δ U = 4 R T_{0}$

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