A). A cylindrical piston (shown below) is compressed from 30 to 20 cm and the pi

Question

A). A cylindrical piston (shown below) is compressed from 30 to 20 cm and the piston is placed
inside an infinite bath at 25 degree C (piston walls are diathermal). The air inside the cylinder can be treated as an ideal gas and has an initial pressure before compression of 1 atm. How much work is required to complete the compression from 30 to 20 cm?

B). Now imagine that the walls of the cylinder are adiabatic. What is the minimum work required to

complete the same compression in (a) when the piston walls are adiabatic?

A). A cylindrical piston (shown below) is compressed from 30 to 20 cm and the piston is placed inside an infinite bath at 25 degree C (piston walls are diathermal). The air inside the cylinder can be treated as an ideal gas and has an initial pressure before compression of 1 atm. How much work is required to complete the compression from 30 to 20 cm? B). Now imagine that the walls of the cylinder are adiabatic. What is the minimum work required to complete the same compression in (a) when the piston walls are adiabatic?

Explanation / Answer

1) If the walls are diathermal, the temperature can change and you can assume this is a constant-pressure process. In that case:

W = -P(V2-V1)

V= r2*h*pi

V1 = 0.102 * 0.30 * pi = 0.00942 m3

V2 = 0.102 * 0.20 * pi = 0.00628 m3

P = 1 atm or 101325 Pa

W = - 101325 Pa * (0.00628-0.00942) = 318.2 J

T1 = 25

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