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Question

Two moles of an ideal monoatomic gas undergoes a process 1 - 2 - 3 as shown in figure. Then total heat supplied to the gas in the process is

Difficult

A

$2 R T_{0} (1 + \ln 4)$
B

$4 R T_{0} \ln 2$
C

$5 R T_{0}$
D

$R T_{0} (3 + \ln 16)$

Solution

(4)
$\begin{array}{l} Q_{12} = H e a t \sup p l i e d in t h e p r o c e s s 1 - 2 \\ = 2 \times \frac{3 R}{2} \times (2 T_{0} - T_{0}) = 3 R T_{0} \\ \Pr o c e s s 2 - 3 i s i s o t h e r m a l . T h e r e f o r e h e a t \sup p l i e d t o \\ t h e g a s, Q_{23} = W o r k d o n e b y t h e g a s \\ = P_{2} V_{2} \ln (\frac{V_{3}}{V_{2}}) \\ = n R T_{2} \ln (\frac{V_{3}}{V_{2}}) = 2. R . 2 T_{0} \ln (\frac{V_{0}}{V_{0}}) \\ ∴ Q_{23} = 4 R T_{0} \ln (2) \\ ∴ T o t a l h e a t \sup p l i e d t o t h e g a s \\ = Q_{12} + Q_{23} = R T_{0} (3 + \ln 16) \end{array}$

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