For an ideal gas the instantaneous change in pressure P with volume V is given by the equation d P d V = - a P . If P = P 0 at V = 0 is the given boundary condition, then the maximum temperature one m

Question

For an ideal gas the instantaneous change in pressure P with volume V is given by the equation d P d V = - a P . If P = P 0 at V = 0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here R is the gas constant)

TestHub · Accepted Answer

d P d V = - a P ∫ P 0 P d P P = - ∫ 0 v a d V ⇒ ln P P 0 = - a V P = P 0 e - a V Now, P V = R T (as n = 1 ) P + V d P d V = R d T d V [ for maximum T , d T d V = 0 ] P - a P V = 0 ⇒ V = 1 a Thus, T = P V R = P 0 e - 1 R a = P 0 e R a

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