Question

As shown in Fig. P2.56, a gas contained within a piston–
cylinder assembly, initially at a volume of 0.1 m3, undergoes
a constant-pressure expansion at 2 bar to a final volume of
0.12 m3, while being slowly heated through the base. The
change in internal energy of the gas is 0.25 kJ. The piston
and cylinder walls are fabricated from heat-resistant material,
and the piston moves smoothly in the cylinder. The local
atmospheric pressure is 1 bar.


(a) For the gas as the system, evaluate work and heat transfer,
each in kJ.

Answer 1

(a)

Gas as the system:

Calculate the work done during the constant-pressure expansion process.

Here, p is the constant pressure, is the volume at state 1, and is the volume at state 2.

Substitute for, for and for.

Therefore, the work transfer from the gas system is.

Apply energy balance to the gas as the system.

…… (1)

Here, heat input to the system is and work transfer from the system is.

Apply the equation for change in total energy of gas as the system.

…… (2)

Here, change in internal energy is, change in kinetic energy of the system is and change in potential energy of the system is.

Equate the equations (1) and equation (2).

Neglect the kinetic and potential energy changes and write the reduced expression.

Substitute for and for in above equation.

Therefore, the heat transfer to the gas as the system is.

(b)

Piston as the system:

Draw the free body diagram of the piston, assuming there is no friction between the piston and cylinder walls.

Consider the equilibrium of forces in the vertical direction.

Here, F is the weight of the piston acting on the gas.

To move the piston in vertically upward direction, we need to overcome the weight of the piston F.

Calculate the work done during the expansion process considering piston as the system.

Here, F is the force acting on the piston, is the atmospheric pressure, A is the area of the piston, and dz is the distance moved by the piston.

Substitute for, for and for.

Therefore, the work done on the piston is.

Calculate the change in potential energy.

Apply energy balance to the piston.

Here, change in internal energy is, change in kinetic energy of the system is and change in potential energy of the system is.

Substitute 0 for , 0 for , 0 for , and -2 kJ W.

Therefore, the change in potential energy of the piston is.

The total energy balance is shown in the following table.