Question

An ideal gas with γ = 1.400 expands adiabatically from a pressure of 365.0 Pa and a volume of 70.00 m3 , doing 101.0 J of work while expanding to a final volume. What is its final pressure-volume product?

Answer #1

In adiabatic process,

p V^Y = C (a constant)

Now, initial values of p = 365.0 Pa.

V = 70.0 m^3

and Y = 1.40

So, C = 365*70^1.4 = 139775.2

Now, work done in adiabatic process is given by

W = C/(Y-1) * [1/V1^(Y-1) - 1/V2^(Y-1)]

W = (C/0.4) * (1/V1^0.4 - 1/V2^0.4)

put the vaues -

101 = (139775.2 /0.4)(1/70^0.4 - 1/V2^0.4)

=> (1/70^0.4 - 1/V2^0.4) = 2.89 x 10^-4

=> 0.18279 - 1/V2^0.4 = 0.000289

=> 1/V2^0.4 = 0.182501

=> V2^0.4 = 5.479

=> 0.4 In(V2) = 1.70

=> In(V2) = 4.2525

=> V2 = 70.2808 Pa.

So, p2 = 139775.2 / (70.2808)^1.4 = 363 Pa

So, final pressure-volume product = p2V2 = 363*70.2808 = 25510 Pa.m^3

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