First and Second Law of Thermodynamics Solved Questions

Note: For the following examples, Appendix B for steam values that I have referred to were obtained from: 

M.D Koretsky, Engineering and Chemical Thermodynamics, Wiley, 2004.

Example 1

2 Kgs of steam at 800 kPa and 600°C is contained in a piston-cylinder assembly. Calculate the work if:

a) The steam expands reversibly and isothermally to 300 kPa.

b) The steam expands reversibly and adiabatically to 300 kPa.

Solution

System: Contents of the piston cylinder assembly

a) The work done by the system is calculated as follows:

It is necessary to plot a P versus V graph and calculate the area under the curve. 

Since expansion occurs at T = 600°C, then the variation of V as a function of P can be determined from the steam table as follows:

The plot of P versus V is shown in the figure below. (Plotted using MathCAD)

The area under the curve can be solved using the trapezoidal rule:

Alternatively, the work done by the system can be solved using the 1st law of thermodynamics: 

From Appendix B

b) The 1st law of thermodynamics simplifies as:

Since the process is reversible and adiabatic (or isentropic), the entropy remains constant at a value of 8.1332 kJ/kg.K. Therefore, the properties at the final state are:

Substituting these values into equation3:

Example 2

Consider the system shown in the figure below:

The piston is made of a non-heat-conducting material and the tank is insulated. Initially, the piston is at the extreme left-hand-side of the cylinder and the cylinder contains 1.5 kg of steam at 200°C and 100 kPa. The cylinder is connected to an infinite source of air at 500 kPa and 250°C, and the valve is opened slightly until the pressure in the cylinder reaches 500 kPa.

a) Calculate the final temperature of the air under these conditions.

b) Calculate the final temperature of the air if a small cooling coil is placed in the cylinder to maintain the steam temperature constant at 200°C.

Solution

Let the subscripts A and S stand for air and steam, respectively.

Since steam occupies the whole volume of the cylinder initially, the volume of the cylinder is calculated from the initial conditions. From Appendix B (Table B.4)

Thus:

a) The steam in the cylinder undergoes a reversible and adiabatic compression,

b) In this case, the steam in the cylinder undergoes a reversible and isothermal compression. Thus, the properties of the steam at the final state are:

Considering the air in the cylinder as a system, the unsteady-state mass and energy balances again lead to: