### What is the final temperature of the gas

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The following are first law problems in Thermodynamics:

1. The molar energy of a mono atomic gas which obeys van der waals equation is given by:

E =(3/2)*RT - (a/V)

where V is the molar volume at temperature T, and a is a constant. Initially one mole of the gas is at temperature T1 and occupies volume V1. The gas is allowed to expand adiabatically into a vacuum so that it occupies a total volume V2.

What is the final temperature of the gas?

2. One mole of a perfect gas performs a quasi static cycle which consists of the following 4 stages:

1. from the state (P1,V1) at constant pressure to the state (P1,V2)

2. At constant volume to the state (P2,V2)

3. at constant pressure to P2,V1)

4, At constant volume back to the initial state (P!,V1.

Find: a) the work done on the gas in the cycle and the heat absorbed by the gas in the cycle.

3. The same as Problem 2 with the following 4 stages:

1. at constant volume from T1,V1) to (T2,V1)

2. isothermally to (T2,V2)

3. at constant volume to (T1,V2)

4. Isothermally back to (T1,V1)

Find: a) the work done on the gas in the cycle and the heat absorbed by the gas in the cycle.

4. calculate the change in internal energy when 1 mole of liquid water at 1 atm and 100degrees C is evaporated to water vapor at the same temp. and pressure, given that the molar volumes of the liquid and vapor under these conditions are: 18.8 cm^3/mol and 30200 cm^3/mol respectively and the latent heat of vaporization is 40600J/mol

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