Question

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

• A. $75\text{K}$
• B. $300\text{K}$
• C. $560\text{K}$
• D. $340\text{K}$

Answer 1

The correct option is A $75\text{K}$

Given,
Gas is ideal and monoatomic, so $\gamma =\frac{5}{3}$
Gas is undergoing adiabatic expansion, so the equation of state of the gas in terms of $T$ and $V$ is given by
$T{V}^{\gamma -1}=k$
From this, we can write that
$T_i{V}_i^{\gamma -1}=T_f{V}_f^{\gamma -1}$
or $T_f=T_i{\left(\frac{V_i}{V_f}\right)}^{\gamma -1}$
From the data given in the question,
$T_f=300\times {\left(\frac{V_i}{8V_i}\right)}^{\frac{5}{3}-1}=\frac{300}{4}=75\text{K}$
Hence, option (a) is the correct answer.