First slide

Thermodynamic processes

Question

Dry air $(γ = \frac{3}{2})$ at atmospheric pressure is suddenly compressed to ${\frac{1}{4}}^{th}$ of its original volume, the pressure will be

Moderate

A

10 atm
B

8 atm
C

3 atm
D

6 atm

Solution

$\begin{array}{rcl} {Pressure P}_{1} =P=1 atm \\ t o f i n d P_{2} \\ g i v e n v o l u m e V_{1} {=V and :V}_{2} = \frac{V}{4} \\ a d i a b a t i c p r o c e s s (i t i s a s u d d e n p r o c e s s) r e l a t i o n b e t w e e n P a n d V i s {PV}^{γ} =Constant \\ \frac{P_{1}}{P_{2}} = {(\frac{V_{2}}{V_{1}})}^{γ} \\ s u b s t i t u t e t h e g i v e n v a l u e s i n a b o v e e q u a t i o n \\ \frac{P}{P_{2}} = {(\frac{\frac{V}{4}}{V})}^{\frac{3}{2}} \\ \Rightarrow & \frac{P}{P_{2}} = \frac{1}{8} \\ P_{2} & = & 8 P given P= 1 atm \\ \Rightarrow & P_{2} =8 atm \end{array}$

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