First slide

Thermodynamic processes

Question

During an adiabatic process, the pressure of gas is found to be proportional to the cube of its temperature. The ratio of $s p e c i f i c h e a t r a t i o γ$ for the gas is

Moderate

A

$2$
B

$\frac{5}{3}$
C

$\frac{3}{2}$
D

$\frac{4}{3}$

Solution

$\begin{array}{rcl} in adiabatic process, \\ {relation between pressure P and temperature T is P}^{1-γ} {.T}^{γ} =Constant \\ w h e r e γ i s s p e c i f i c h e a t r a t i o \\ \Rightarrow & {PαT}^{\frac{γ}{γ-1}} \\ {But given PαT}^{3} \\ o n c o m p a r i n g a b o v e t w o e q u a t i o n s \\ \frac{γ}{γ-1} =3 \\ \Rightarrow & γ = 3 γ - 3 \\ \Rightarrow & 2γ=3 \\ \Rightarrow & γ=3/2 \end{array}$

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