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One Mole of an Ideal Gas Undergoes a Process P = P 0 1 + ( V V 0 ) 2 Where P 0 and V 0 Are Constants . Find the Temperature of the Gas When V = V 0 . - Physics

Sum

One mole of an ideal gas undergoes a process `P = (P_0)/(1+(V/V_0)^2` where `p_0` and `V_0` are constants . Find the temperature of the gas when `V=V_0` .

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Solution

Given : 

`P = (p_0)/(1+(V/V_0)^2`

Multiplying both sides by V, we get

`pV = (p_0V)/(1+(V/V_0)^2)`

`pV = RT`              [From eq. (1)]        

Now , 

`RT = (p_0V)/(1+(V/V_0)^2)`

`T = 1/R ((p_0V_0)/(1+(V_0/V_0)^2))`       [`V=V_0`]

⇒ `T = (p_0V_0)/(2R)`

Concept: Kinetic Theory of Gases and Radiation - Kinetic Interpretation of Temperature
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 2 Kinetic Theory of Gases
Q 38 | Page 36
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