First slide

Thermodynamic processes

Question

A mono atomic gas ( $γ$ =5/3) is suddenly compressed to 1/8th of it’s volume adiabatically then the pressure of the gas will change to (times the initial pressure):

Moderate

A

24/5
B

8
C

40/3
D

32

Solution

$\begin{array}{rcl} i n a n a d i a b a t i c p r o c e s s \\ P_{1} V_{1}^{γ} & = & P_{2} V_{2}^{γ} - - - (1) \\ h e r e P_{1}, P_{2} a r e i n i t i a l a n d f i n a l p r e s s u r e o f t h e g a s \\ V_{1}, V_{2} a r e i n i t i a l a n d f i n a l v o l u m e o f t h e g a s \\ γ i s s p e c i f i c h e a t r a t i o & = & \frac{5}{3} \\ i f V_{1} & = & 1, t h e n V_{2} = \frac{1}{8} \\ \Rightarrow & P_{2} {=P}_{1} {(\frac{V_{1}}{V_{2}})}^{γ} from equation (1) \\ \Rightarrow & P_{2} {=P}_{1} {(\frac{1}{\frac{1}{8}})}^{\frac{5}{3}} \\ \Rightarrow & P_{2} {=P}_{1} {(8)}^{\frac{5}{3}} \\ \Rightarrow & P_{2} {=P}_{1} {(2)}^{5} \\ \Rightarrow & P_{2} {=P}_{1} (32) \end{array}$

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