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Question
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)`
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