Question

In an adiabatic change, the pressure and temperature of a monoatomic gas are related with relation as $P\propto T^C$, where $C$ is equal to :

• A. $\frac{5}{4}$
• B. $\frac{5}{3}$
• C. $\frac{5}{2}$
• D. $\frac{3}{5}$

Answer 1

Answer: (C)

$\frac{5}{2}$

$Pk{T}^C$ $\Rightarrow$ $P{T}^{-C}=k$
For adiabatic change
$P{V}^{\gamma }=$ constant [where $\gamma$ is $\frac{C_p}{C_v}$]
or $P{T}^{\gamma /1-\gamma }=$ constant
Comparing it with the given relation
$\frac{\gamma }{1-\gamma }=-C$
$\frac{\gamma }{\gamma -1}=C$
For monoatomic gas, $\gamma =\frac{5}{3}$
$\frac{5/3}{\frac{5}{3}-1}=C$ $\Rightarrow$ $C=\frac{5}{3}\times \frac{3}{2}=\frac{5}{2}$