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:

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) (1/2) (B) 2 (C) √2 (D) (1/√2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9a8d5702a4bb9a162b669687e5a41c3b-.png" /> PV 1 / 2= c ( nRT / V ) V 1 / 2= c T = c 1 V 1 / 2 ( T 2/ T 1)=(( V 2/ V 1))1 / 2=((2 V 1/ V 1))1 / 2 ( T 2/ T 1)=√2

Q. 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:

$\frac{1}{2}$

2

$2$

$\frac{1}{2}$

$P V^{1/2} = c$
$\frac{n RT}{V} V^{1/2} = c$
$T = c^{1} V^{1/2}$
$\frac{T _{2}}{T _{1}} = (\frac{V _{2}}{V _{1}})^{1/2} = (\frac{2 V _{1}}{V _{1}})^{1/2}$
$\frac{T _{2}}{T _{1}} = 2$

Q. Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2​=2V1​ then the ratio of temperature T2​/T1​ is:

21​

2

2​

2​1​

PV1/2=c VnRT​V1/2=c T=c1V1/2 T1​T2​​=(V1​V2​​)1/2=(V1​2V1​​)1/2 T1​T2​​=2​

Q. 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:

$\frac{1}{2}$

$2$

$\frac{1}{2}$

$P V^{1/2} = c$
$\frac{n RT}{V} V^{1/2} = c$
$T = c^{1} V^{1/2}$
$\frac{T _{2}}{T _{1}} = (\frac{V _{2}}{V _{1}})^{1/2} = (\frac{2 V _{1}}{V _{1}})^{1/2}$
$\frac{T _{2}}{T _{1}} = 2$