# Application of the first law of thermodynamics in some thermodynamic processes (isobaric, isothermal, isochoric)

1. The graph below shows the thermodynamic cycle experienced by a gas. The work done by gas on the process ABCD is …

__Known :__

Pressure 1 (P_{1}) = 2 x 10^{5} Pa

Pressure 2 (P_{2}) = 4 x 10^{5} Pa

Volume 1 (V_{1}) = 1 m^{3}

Volume 2 (V_{2}) = 3 m^{3}

Wanted: Work done by gas on process ABCD (W).

__Solution :__

Work done by a gas is equal to the area of ABCD.

W = (P_{2} – P_{1})(V_{2} – V_{1})

W = (4 x 10^{5} – 2 x 10^{5})(3 – 1)

W = (2 x 10^{5})(2)

W = 4 x 10^{5} Joule

2. The work done by gas on process ABC is…

__Known :__

Pressure 1 (P_{1}) = 3 x 10^{5} Pa

Pressure 2 (P_{2}) = 6 x 10^{5} Pa

Volume 1 (V_{1}) = 20 cm^{3} = 20 x 10^{-6} m^{3}

Volume 2 (V_{2}) = 60 cm^{3} = 60 x 10^{-6} m^{3}

__Wanted __: The work done by gas on process ABC

__Solution :__

Work done by gas = area of ABC.

W = ½ (P_{2} – P_{1})(V_{2} – V_{1})

W = 1/2 (6 x 10^{5} – 3 x 10^{5})(60 x 10^{-6} – 20 x 10^{-6})

W = 1/2 (3 x 10^{5})(40 x 10^{-6})

W = 1/2 (120 x 10^{-1} Joule)

W = 1/2 (12 Joule)

W = 6 Joule

3. PV diagram for a gas in a closed container shown in figure below. The work done by the gas is shown in which process.

Solution

Process AB and process DC are isobaric processes (the pressure is kept constant). Process AD and process BC are isochoric processes (volume does not change).

The work was done by gas when the gas expands (process DC).