Thermodynamic process is shown below on a P - V diagram for one...

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 $\dfrac{{T}_{2}}{{T}_{1}}$ is :

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

Options

A $\sqrt{2}$
B $\dfrac{1}{\sqrt{2}}$
C $\dfrac{1}{2}$
D $2$

Correct answer

A. $\sqrt{2}$

Step-by-step solution

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

$P{V}^{1 / 2} = c$

$\dfrac{nRT}{V}{V}^{1 / 2} = c$

$T = {c}^{1}{V}^{1 / 2}$

$\dfrac{{T}_{2}}{{T}_{1}} = {\left(\dfrac{{V}_{2}}{{V}_{1}}\right)}^{1 / 2} = {\left(\dfrac{2{V}_{1}}{{V}_{1}}\right)}^{1 / 2}$

$\dfrac{{T}_{2}}{{T}_{1}} = \sqrt{2}$

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