Question

A closed system contains 1kg of air initially at 100kPa, 30 deg Celsius and 0.5m3.The air expands reversibly and isothermally until the volume of the system doubles.For the process determine the enthropy change and the heat transfer of the air being expanded,

Answer 1

The essential difference between the expansion in an closed system and the reversible isothermal expansion of an 1kg gas can also be captured clearly in terms of entropy changes.

For a state change from initial volume V₁ and temperature T_1, to final volume V₂ and (the same) temperature T_1, the entropy change is given by

Using equation of state and in isothermal process for an isothermal process,

There entropy is

Now applying the values

V_{1 =} 0.5 m³ =500 L

V₂ = 500x2= 1000 L

N= PV/RT

10⁵ Pa x 0.5 m³

^{= ----------------------------}

   8.31 J/mol^-1 x 303K

1 bar x 500 L

= ---------------------------

0.0831 L-bar/mol-K x 303K

= 19.8 moles

Now

=(19.8 mol)x(8.31 J/mol^-1K) ln (1000/500)

=114 J/K

Entropy is 114 J/K

b) if the temperature is held constant, the internal energy of the system also is constant, and so . Since the First Law of Thermodynamics states that , it follows that for the isothermal compression or expansion of ideal gases.

Therefore,the heat transferred to the gas is

.

Heat transfered is also 114 J/K