Question

An ideal monatomic gas at $300K$ expands adiabatically to 8 times its volume. What is the final temperature?

• A. 75 K
• B. 300 K
• C. 560K
• D. 340K K

Answer 1

Answer: (A)

75 K

Solution:- (A) $75K$

For an adiabatic process,

$T{V}^{\gamma -1}=\text{constant}$

$\therefore \frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$

Given:-

$T_1=300K$

$T_2=T\left(\text{say}\right)=?$

$V_1=V$

$V_2=8V$

$\gamma =\frac{5}{3}(\because \text{the gas is monoatomic})$

$\therefore \frac{T}{300}={\left(\frac{V}{8V}\right)}^{\frac{5}{3}-1}$

$\Rightarrow \frac{T}{300}={\left(\frac{1}{8}\right)}^{\frac{2}{3}}$

$\Rightarrow T=\frac{300}{4}=75K$

Hence the final temperature will be $75K$.