Question

Two moles of an ideal monoatomic gas occupy a volume $2V$ at temperature $300K$ , it expands to a volume $4V$ adiabatically, then the final temperature of gas is

• A. $179K$
• B. $189K$
• C. $199K$
• D. $219K$

Answer 1

Answer: (B)

Since in an adiabatic process $T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$T_2=T_1{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}=300{\left(\frac{2V}{4V}\right)}^{\left(\frac{5}{3}-1\right)}$
$[\because V_1=2V$ and $V_2=4V$ for monotonic gas $\gamma =\frac{5}{3}]$
$=300{\left(\frac{1}{2}\right)}^{2/3}=\frac{300}{2^{2/3}}$
$=188.98\approx 189K$