Thermodynamics - Find final pressure

In summary, using linear interpolation and steam tables, the final pressure of the steam undergoing a constant volume process can be estimated to be 93.4 kPa when initially at a specific volume of 0.001 m^3/kg at 0.1 MPa and 350°C, and at a specific volume of 0.001088 m^3/kg and pressures of 0.1 MPa and 0.2 MPa at 300°C.
  • #1
Ribz
2
0

Homework Statement



An amount of steam undergoes a constant volume process from an initial state for which the pressure and temperature are 0.1MPa and 350°C respectively. The final temperature is 300°C. Using linear interpolation estimate the final pressure.

Homework Equations



Use Thermodynamics and Transport Properties of Fluids

The Attempt at a Solution



I used linear interpolation for the pressure at 100°C, which was 1.01325 bar. Got my answer which was 28.3 kPa. The answer stated is 93.4 kPa
 
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  • #2
Ribz said:

Homework Statement



An amount of steam undergoes a constant volume process from an initial state for which the pressure and temperature are 0.1MPa and 350°C respectively. The final temperature is 300°C. Using linear interpolation estimate the final pressure.

Homework Equations



Use Thermodynamics and Transport Properties of Fluids

The Attempt at a Solution



I used linear interpolation for the pressure at 100°C, which was 1.01325 bar. Got my answer which was 28.3 kPa. The answer stated is 93.4 kPa
Hi Ribz. Welcome to Physics Forums!

Let me guess. You are supposed to be using steam tables to solve this, correct?

What is being held constant in this system:
(a) specific enthalpy?
(b) specific volume?
(c) specific internal energy?
(d) specific entropy?

Chet
 
  • #3
Specific volume is constant
 
  • #4
Ribz said:
Specific volume is constant
Good. So, from your steam tables, what is the specific volume of the steam initially? Now look in your steam tables for 300C, and find a condition as close as you can get to this specific volume. What is the specific volume at that point, and at the two adjacent pressures in the table? What are the pressures and volumes that go with the three points in your table?

Chet
 
  • #5


I would like to provide a more detailed response to this problem. Firstly, it is important to note that the given problem involves a constant volume process, meaning that the volume of the steam remains constant throughout the process. This indicates that the work done by the steam is equal to zero, as there is no change in volume. Therefore, the first law of thermodynamics reduces to ΔU = Q, where ΔU is the change in internal energy and Q is the heat added to the system.

Next, we can use the ideal gas law, PV = nRT, to relate the pressure and temperature of the steam. Since the volume is constant, we can rearrange the equation to get P = (nR/V)T.

Using this equation, we can calculate the final pressure by finding the ratio of the initial and final temperatures and multiplying it by the initial pressure. This would give us a final pressure of 0.1 MPa * (300/350) = 0.0857 MPa.

However, the problem also states to use linear interpolation to estimate the final pressure. This means that we need to consider the change in pressure as the temperature changes from 350°C to 300°C. To do this, we can use the ideal gas law again, but this time with the initial and final temperatures and pressures.

P1V1 = P2V2

where P1 = 0.1 MPa, V1 = constant, P2 = final pressure, and V2 = constant.

Rearranging this equation, we get P2 = (P1V1/V2) * (T2/T1)

Substituting in the given values and using the fact that V1 = V2, we get P2 = 0.1 MPa * (300/350) = 0.0857 MPa.

This final pressure is slightly lower than the one calculated using the initial and final temperatures, which is expected as the pressure decreases with decreasing temperature in a constant volume process.

In conclusion, the final pressure of the steam is estimated to be 0.0857 MPa or approximately 85.7 kPa. This is a more accurate answer than the one obtained by simply using linear interpolation at 100°C, as it takes into account the change in pressure with respect to temperature.
 

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, energy, and work.

2. What is the final pressure in thermodynamics?

The final pressure in thermodynamics is the equilibrium pressure that a system reaches after undergoing a change in temperature, volume, or number of particles.

3. How do you find the final pressure in thermodynamics?

The final pressure can be found using the ideal gas law, which states that the product of pressure and volume is proportional to the product of temperature and number of moles of gas. This can also be calculated using other thermodynamic equations, such as Boyle's Law or Charles' Law.

4. What factors influence the final pressure in thermodynamics?

The final pressure is influenced by various factors, including the initial pressure, temperature, volume, and number of moles of gas. It can also be affected by external factors such as pressure changes or changes in the amount of gas in the system.

5. Why is it important to calculate the final pressure in thermodynamics?

Calculating the final pressure is important for understanding how a system will behave under different conditions and for predicting the behavior of gases in various scenarios. It is also crucial for industries such as engineering and chemistry, where precise control of pressure is necessary for reactions and processes.

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