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The equation of state of a gas is PV=nRT(1-B/V),where R is the constant and B is a function of temperature alone.show that the workdone by one mole of this gas during a quasi static isothermal expansion from initial volume Vi to Vf.

The equation of state of a gas is PV=nRT(1-B/V),where R is the constant and B is a function of temperature alone.show that the workdone by one mole of this gas during a quasi static isothermal expansion from initial volume Vi to Vf.

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Vikas TU
14149 Points
one year ago
Dear student
W = 2.3026 RT log10 (V2/V1)
According to first law of thermodynamics, heat used up for the expansion of gas = W/J
So, H = 2.3026 (RT/J) log10 (V2/V1)
Since P1V1 = P2V2, thus, V2/V1= P1/P2
Substituting forV2/V1, H = 2.3026 (RT/J) log10 (P1/P2)
On the other hand, if the gas is compressed, the work is done on the gas and is therefore negative. The work done for isothermal compression is given by,
W = -2.3026 RT log10 (V2/V1)
So, W =2.3026 RT log10 (V1/V2)
Therefore, H = 2.3026 (RT/J) log10 (V1/V2)
and H = 2.3026 (RT/J) log10 (P2/P1)
Good Luck 
 

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