How to Tackle Thermodynamics Homework Challenges?

[Andreii]

Hi everyone
Im trying to do three taskes for thermodynamics but I would like to please for some help. First, I have done already and I need just someone to check it if is correctly. Second task - I have drawed the diagram, I believe it is correct, but I have problems on first step of solving it out already. For the third one - I haven't done anything because I don't understand it, not even how to draw the diagram (p-V). Let's go one by one

1. Task:

Homework Statement

In the tub is water with mass 5 kg and temeprature 20 C (celzius – degrees). We put into the tub piece of ice that has a mass of 1 kg and temeprature – 27 C. What is the final temperature of the water if we presume that the system water-ice is adiabatic? Use firstlaw of thermodynamics.

Homework Equations

The Attempt at a Solution

Two specific heats:
$$c_{water}$$ = 4,182 kJ/kgC (i do it in celzius degrees and not Kelvins, the constant ''c'' should stay the same?)
$$c_{ice}$$ = 2,1 kJ/kgC

$$q_{ice}$$ = 335 kJ/kg

$$Q_{fromSystem}$$ = $$Q_{toSistem}$$

$$m_{water}$$ * $$c_{water}$$ * ( $$T_{water}$$ - $$T_{2}$$ ) = $$m_{ice}$$ * $$c_{ice}$$ * ( $$T_{1}$$ - $$T_{ice}$$ ) + $$m_{ice}$$ * $$q_{ice}$$ + $$m_{ice}$$ * $$c_{ice}$$ * ( $$T_{2}$$ - $$T_{1}$$ )

$$T_{2}$$ = $$\frac{c_{water} * m_{water} * T_{water} + c_{ice} * m_{ice} * T_{ice} - m_{ice} * q_{ice}}{c_{water} * m_{ice} + c_{water} * m_{water}}$$


$$T_{2}$$ = $$\frac{4,182 kJ/kgC * 5 kg * 20 C + 2,1 kJ / kgC * 1 * (-27 C) - 1 kg * 335 kJ/kg}{4,182 kJ/kgC * 1 kg + 4,182 kJ/kgC * 5 kg}$$

$$T_{2}$$ = 1,06 C

Is this correct?

2. Task:

Homework Statement

In the vapor's turbine with power 6 MW expand vapor from pressure 65 bar and temperature 360 C on the pressure 0,05 bar. Interior thermal efficiency of turbine is 0,86. Determinate how much vapor expands. Determinate also quality ('' x '') of the vapor. What is thermal efficiency if vapor expands adiabatic to quality 0,88 and pressure 0,05 bar.

Homework Equations

The Attempt at a Solution

The P-V diagram, which I drawed for this task, is http://img.photobucket.com/albums/v309/Andreii/grafek.jpg

Thermal efficiency:

$$\eta$$ = $$\frac{W_{t12}}{W_{t12*}}$$ = $$\frac{h_{1} - h_{2}}{h_{1} * h_{2*}}$$

Where $$h_{2*}$$ is function of ($$s_{1}$$, $$p_{2}$$)

s = entropy
p = pressure

Enthalphy (I need it for therman efficiency):

From the Mollier diagram for water's vapor, I got the following data:

$$h_{1}$$ ($$T_{1}$$, $$p_{1}$$) = $$h_{1}$$ (360 C, 65 bar) = 3050 kJ/kg

So far, enthalphy for temperature 360 C at 65 bar looks OK. I understand the task (second one) until here.
After this step (yes I know, I am not even at the beginning of the determinating the task) the problems begin:
I need another enthalpy: 360 C at 0.05 bar. My Mollier's diagram don't show this OR I don't know what to do in this case. I have tried to graphically show what's wrong in the program Painter. The reason why I cannot get another enthalpy is http://img.photobucket.com/albums/v309/Andreii/mollie.jpg
I also have the book: Fundamentals of engineering thermodynamics (5th edition) (Authors: Wiley, Moran, Shapiro) but I cannot help myself much with the latest few pages where are numbers (enthalphy, entropy,...) for specific case (given temperature, pressure,...) already written.

3. Task:

Homework Statement

For the open process of gas turbine and isobaric entry of heat, we know:
- at the entrance to the compressor is pressure 1 bar and temperature 100 C
- pressure's relation: ﻉ = 8
- at the entrance to the turbine is temperature 1100 C
- expansion and compression are politropic with n = 1,2. We ''work'' with air.
Determinate the temperatures and pressured in all four caracteristic points. Determinate also work, change of heat and thermal efficiency of process. What is mass' stream of the air if power of turbine is 10 MW? Draw the whole equipment used, draw also diagram (p-V).

Not sure what to do here. I figured out that I need to draw into diagram circle process - forth point will end in the first one. In this task, I prolly don't need to search in Mollier's diagram or in tables in the mentoined book. Everything I need to do after I have p-V diagram is using needed formulas. Sketch of equipment prolly isn't so hard to do.

Thank you for any answers!

 

[Jhero]

Hi there,

I am happy to help with your thermodynamics tasks. For the first task, your solution looks correct to me. You have correctly used the first law of thermodynamics and the specific heat values to determine the final temperature. Good job!

For the second task, you are on the right track. You will need to use the enthalpy values for the given temperature and pressure to calculate the thermal efficiency. However, for the second enthalpy value, you will need to use the saturation temperature at the given pressure (0.05 bar). You can find this value in tables or use an online calculator. Once you have the second enthalpy value, you can continue with your calculations. Also, make sure to convert the temperatures to Kelvin before using them in calculations.

For the third task, you are correct in drawing the p-V diagram. You will need to use the equations for isentropic processes to determine the temperatures and pressures at each point. You can also use the given pressure ratio and temperature at the turbine entrance to solve for the other values. The mass flow rate can be determined using the power and enthalpy values at the turbine entrance. Make sure to also convert the temperatures to Kelvin before using them in calculations.

I hope this helps. Let me know if you have any further questions or need clarification on any of the steps. Good luck with your tasks!