Question

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If $V _{2}=2 V _{1}$ then the ratio of temperature $T _{2} / T _{1}$ is:

• A. $\frac{1}{2}$
• B. 2
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

$PV ^{1 / 2}= c$
$\frac{ nRT }{ V } V ^{1 / 2}= c$
$T = c ^{1} V ^{1 / 2}$
$\frac{ T _{2}}{ T _{1}}=\left(\frac{ V _{2}}{ V _{1}}\right)^{1 / 2}=\left(\frac{2 V _{1}}{ V _{1}}\right)^{1 / 2}$
$\frac{ T _{2}}{ T _{1}}=\sqrt{2}$