First slide

Thermodynamic processes

Question

In an adiabatic change, the pressure and temperature of a mono atomic gas are related as ${PαT}^{C}$ , where c equals

Moderate

A

$\frac{2}{5}$
B

$\frac{3}{5}$
C

$\frac{5}{2}$
D

$\frac{5}{3}$

Solution

$\begin{array}{rcl} i n a d i a b a t i c p r o c e s s r e l a t i o n b e t w e e n P r e s s u r e P, T e m p e r a t u r e T i s P^{1 - γ} T^{γ} & = & c o n s \tan t \\ \Rightarrow & \frac{T^{γ}}{P^{γ-1}} = Constant \\ \Rightarrow & P^{γ-1} α T^{γ} \\ \Rightarrow & P α T^{\frac{γ}{γ - 1}} \\ g i v e n {PαT}^{C} \\ o n c o m p a r i n g t h e a b o v e t w o e q u a t i o n s \\ C= \frac{γ}{γ - 1} \\ f o r m o n o a t o m i c g a s s p e c i f i c h e a t r a t i o γ & = & \frac{5}{3} \\ s u b s t i t u t e γ i n a b o v e e q u a t i o n o f C \\ C = \frac{\frac{5}{3}}{\frac{5}{3} - 1} \\ \Rightarrow & C = \frac{5}{2} \end{array}$

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