Steam in a cylinder-piston arrangement expands from an initial condition of 5 bar, 80% dry to a final state of 2 bar, dry saturated steam.

The initial volume of steam is 0.8 m3.
The process of expansion can be represented by a straight line on the p–Vdiagram.

5B. What is the mass of steam in the system, in kg?

5C. What is the work done by the system, in kJ?

5D. What is the change in energy of the system, in kJ?

5E. What is the heat absorbed by the system, in kJ?

5F. Which of the following assumptions did you have to make

The process is adiabatic.

The process is reversible.

All work interaction is of the expansion type.

Only thermal energy change is significant.

The behaviour of the contents of the system is like that of an ideal gas.

for 5f -

All work interaction is of the expansion type.

Only thermal energy change is significant.

these two apply. becoz the process itself is expansion only as stated in problem and only significant change which we can notice is temperature which lowers as expansion gets done

50kg

To answer the given questions, we need to follow a step-by-step procedure and use the appropriate equations. Let's proceed with each question one by one:

5B. What is the mass of steam in the system, in kg?
To find the mass of steam, we can use the ideal gas equation:

PV = mRT

Where:
P = pressure (in this case, 5 bar and 2 bar)
V = volume of the steam (0.8 m^3)
m = mass of the steam (to be determined)
R = specific gas constant for steam
T = temperature of the steam (to be determined)

Since the steam is saturated, we can determine the temperature using the saturation tables (specifically the temperature corresponding to the given pressure of 2 bar).

Once we have the temperature, we can rearrange the ideal gas equation to solve for the mass:
m = PV / (RT)

Substituting the given values, we can calculate the mass of steam in the system.

5C. What is the work done by the system, in kJ?
The work done by the system during expansion can be calculated using the formula:

W = ∫PdV

Since the expansion process is represented by a straight line on the p-V diagram, we can calculate the area under the curve. In this case, the area under the line represents the work done by the system. We can use the formula for the area of a trapezoid to calculate it:

W = (P1 + P2) * (V2 - V1) / 2

Where:
P1 = initial pressure (5 bar)
P2 = final pressure (2 bar)
V1 = initial volume (0.8 m^3)
V2 = final volume (determined by the process)

Substituting the given values, we can calculate the work done by the system.

5D. What is the change in energy of the system, in kJ?
The change in energy of the system can be calculated as the difference between the initial and final energy states. It can be expressed as:

ΔU = m * (u2 - u1)

Where:
ΔU = change in energy of the system (to be determined)
m = mass of the steam (determined in question 5B)
u1 = specific internal energy at the initial state (determined using the initial conditions)
u2 = specific internal energy at the final state (determined using the final conditions)

Using the specific internal energy values from the steam tables for the given pressure and dryness fractions, we can substitute the values and calculate the change in energy.

5E. What is the heat absorbed by the system, in kJ?
The heat absorbed by the system can be calculated using the first law of thermodynamics equation:

Q = ΔU - W

Where:
Q = heat absorbed by the system (to be determined)
ΔU = change in energy of the system (determined in question 5D)
W = work done by the system (determined in question 5C)

Substituting the values, we can calculate the heat absorbed by the system.

5F. Which of the following assumptions did you have to make?
Based on the information provided, the assumptions we had to make are:
- The process is adiabatic: No heat transfer occurs between the system and its surroundings.
- The process is reversible: The expansion process can be reversed without any loss of energy or irreversibilities.
- All work interaction is of the expansion type: The only work done is due to the expansion of the steam.
- Only thermal energy change is significant: No other forms of energy transfer, like work or flow work, are significant.
- The behavior of the contents of the system is like that of an ideal gas: Although steam is not an ideal gas, we assume its behavior to be similar to an ideal gas for ease of calculations.