It is proposed that an ideal gas with an initial pressure P1 undergo an isotherm

Question

It is proposed that an ideal gas with an initial pressure P1 undergo an isothermal process during which the volume of the gas is reduced by one-half.

A.) show that s2-s1 is independent of the gas, whereas s2-s1 does depend on the identity of the gas.

B.) could the proposed process take place without violating the second law? If so is it possible to determine whether the process is internally reversible or irreversible? Explain answer.

Could someone also tell me what book is this question from if possible?

Explanation / Answer

a.

We know that

As the isothermal process is internally

s = q/T

s2 - s1 = dq/T

dw = dq = nRT ln(V2/V1)

= nRTln(0.5)

b.

No the process is not violating the second law and the process is internally reversable.

For a internally reversable process the work done is equal to the integral of PdV over a path [ if its less than that it is called as irreversible process] and for an isothermal process work done is equal to the integral of PdV over a path.

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