Nitrogen at an initial state of 420 K, 116 kPa, and 3 m3 is compressed slowly in an isothermal process to a final pressure of 455 kPa. Determine the work done during this process in kJ

-47.5716 kJ

In an isothermal process, temperature is constant and the workdone (W) in compressing a gas from some initial pressure(P₁) and volume (V₁) to some other pressure (P₂) and volume (V₂) is given by;

W = P₁V₁ ln[]              ---------------------(i)

From the question;

Nitrogen gas =

Initial and constant temperature = 420K

initial pressure P₁ = 116 kPa = 116 x 10³ Pa

initial volume V₁ = 3m³

P₂ = 455 kPa = 455 x 10³ Pa

Substitute these values into equation (i) as follows;

W = 116 x 10³ x 3 ln []

W = 116 x 10³ x  3 ln []

W = 348000 ln []

W = 348000 x -1.367

W = -475716 J

Divide the result by 1000 to convert it to kJ

=> W = (-475716 / 1000) kJ

=> W = -47.5716 kJ

Therefore the work done in the isothermal process is -47.5716 kJ

Note: The negative value indicates that work is done on the system.

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explanation: