First slide

Thermodynamic processes

Question

${PV}^{3/2} =$ constant is the relation obeyed by a perfect gas during an adiabatic process, if the initial temperature of the gas is T, then what will be the final temperature of the gas when it is compressed to half of its initial volume.

Moderate

A

$2 T$
B

$4 T$
C

$2^{1/2} T$
D

$2 \sqrt{2} T$

Solution

$\begin{array}{rcl} {given PV}^{3/2} =Constant, for a perfect gas \\ I n a d i a b a t i c p r o c e s s r e l a t i o n b e t w e e n P r e s s u r e P a n d v o l u m e V i s {PV}^{γ} = Constant \\ o n c o m p a r i n g a b o v e t w o e q u a t i o n s \\ \Rightarrow & γ=3/2 \\ g i v e n i n i t i a l t e p e r a t u r e T_{1} =T \\ f i n a l t e m p e r a t u r e T_{2} =? \\ i n i t i a l v o l u m e i s V_{1} =V; \\ {final volume is V}_{2} = \frac{V}{2} \\ I n a d i a b a t i c p r o c e s s r e l a t i o n b e t w e e n t e m p e r a t u r e T a n d v o l u m e V i s {TV}^{γ-1} =Constant \\ T_{1} {V_{1}}^{γ-1} & = & T_{2} {V_{2}}^{γ-1} \\ \frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{γ-1} \\ s u b s t i t u t i n g t h e g i v e n v a l u e s o f T_{1}, V_{1}, V_{2} \\ \frac{T}{T_{2}} = {(\frac{1}{2})}^{1 / 2} \\ T_{2} {=2}^{1/2} T \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App