Question 340: Thermodynamics & KTG

Question

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V
2
= 2V
1
then the ratio of temperature T
2
/T
1
is :
![](https://imagex.cdn.examgoal.net/1kltdwj7n/f56ecefa-34d2-45e2-9d97-1d2a981f1f4a/79854040-7c17-11eb-b0eb-7d97e0807144/file-1kltdwj7o-332w.jpg)

Accepted Answer

From P-V diagram,
Given PV
1/2
= constant ...... (1)
We know that
PV = nRT
$P \propto \left( {{T \over V}} \right)$
Put in equation (1)
$\left( {{T \over V}} \right){(V)^{1/2}}$ = constant
$T \propto {V^{1/2}}$
$ \Rightarrow $ ${{{T_2}} \over {{T_1}}} = \sqrt {{{{V_2}} \over {{V_1}}}} $
$ \Rightarrow $ ${{{T_2}} \over {{T_1}}} = \sqrt {{{2{V_1}} \over {{V_1}}}} $ [As V
2
= 2V
1
]
$ \Rightarrow $ ${{{T_2}} \over {{T_1}}} = \sqrt 2 $

Answer

$\sqrt 2 $

Answer

${1 \over {\sqrt 2 }}$

Answer

${1 \over 2}$

Answer

2

Thermodynamics & KTG

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

Choose the correct answer: