First slide

Thermodynamic processes

Question

The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ changes adiabatically from $(P,δ)$ to $(P^{1} {,δ}^{1})$ . If $\frac{δ}{δ^{1}} = 32$ , then $\frac{P^{1}}{P}$ is:

Moderate

A

$\frac{1}{128}$
B

128
C

32
D

none of these

Solution

$\begin{array}{rcl} a d i a b a t i c r e l a t i o n b e t w e e n P r e s s u r e P a n d v o l u m e V i s \\ {PV}^{γ} =Constant---(1) \\ d e n s i t y (δ) & = & \frac{m a s s (m)}{v o l u m e (V)} \\ \Rightarrow & V = \frac{m}{δ} s u b s t i t u t e i n e q n (1) \\ m a s s i s c o n s \tan t h e n c e, \\ \frac{P}{δ^{γ}} & = & C o n s \tan t \\ \frac{P^{1}}{{(δ}^{γ})^{1}} & = & \frac{P}{δ^{γ}} \\ \frac{P^{1}}{P} = {(\frac{δ^{1}}{δ})}^{γ} \\ s u b s t i t u t e t h e g i v e n v a l u e s \\ \Rightarrow & \frac{P^{1}}{P} = {[\frac{1}{32}]}^{7 / 5} \\ \Rightarrow & \frac{P^{1}}{P} = \frac{1}{2^{7}} \\ \Rightarrow & \frac{P^{1}}{P} = \frac{1}{128} \end{array}$

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