# Thermodynamics - how to go ahead?

1. Feb 2, 2008

### 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 belive 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). Lets go one by one

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
3. 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?

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
3. The attempt at a solution

The P-V diagram, which I drawed for this task, is HERE

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, Im 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 whats wrong in the program Painter. The reason why I cannot get another enthalpy is THIS
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.

1. The problem statement, all variables and given/known data
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.