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Schwarz and John H. Haines, William E. Shampine, I. Find TL, the cycle thermal efficiency, the heat added per kilogram, and the entropy, s, at the beginning of the heat rejection process. Heat is rejected in a constant pressure process also constant T at 20 kPa. Find the heat added to the water per kg water.
How much heat should be added to the water in the heat engine so the refrigerator can remove 1 kJ from the cold space? Show the cycle on a T—s diagram. Determine the coefficient of performance for the cycle. Solution: a T b From Table B. Consider a Carnot-cycle heat pump with R as the working fluid. Find the sign for both the work and the heat transfer. Find the sign for the work and the sign for the heat transfer. Solution: The process is not specified, but the beginning and end states are State 1: Table B.
It is now boiled to become saturated vapor in a reversible process. Find the work term and then the heat transfer from the energy equation.
Find the heat transfer from the entropy equation, is it the same? Energy Eq. Find the work and heat transfer for this process. Solution: Control mass. Solution: C. Find the new v and T. Find the specific heat transfer and the specific work. Solution: Control mass: Energy Eq. It will be compressed in an adiabatic reversible process to kPa and should be 70oC. What should the initial temperature be?
Ra which is a control mass. Entropy Eq. The piston is moved, compressing the water until it reaches a pressure of 1. How much work is required in the process? Water in cylinder. It may be assumed that the expansion is reversible and adiabatic. What was the initial pressure in the cylinder and how much work is done by the water? Process: Rev. Find the final T and the specific heat transfer in this isometric process.
Solution: Energy Eq. Look at the constant v curves in Fig. In the two-phase region they curve slightly and more so in the region above the critical point. A piston compresses the Ra in a reversible, isothermal process until it reaches the saturated vapor state. Calculate the required work and heat transfer to accomplish this process. It is compressed in a reversible adiabatic process to kPa.
How much work is needed? The specific work is measured to be Find the final P and T and show the P-v and the T-s diagram for the process. Water, which is a control mass. The process happens so slowly that the temperature is constant. Find the heat transfer and work for the process assuming it to be reversible. This isobaric process ends when the water has reached a state of saturated liquid.
Find the work and heat transfer and sketch the process in both a P-v and a T-s diagram. H2O Energy Eq. Find the specific work and heat transfer. Estimate the specific work from the area in the P-v diagram and compare it to the correct value. Solution: Continuity Eq. Find the final temperature and the specific work. During the process kJ of work is given out by the ammonia.
What was the initial volume of the cylinder? Control mass with no heat transfer. State 1: Table B. A valve on the vessel is opened, allowing steam to escape.
The overall process is irreversible, but the steam remaining inside the vessel goes through a reversible adiabatic expansion. Determine the fraction of steam that has escaped, when the final state inside is saturated vapor.
The piston is slowly moved to expand the water in an isothermal process to a pressure of kPa. Sketch the process in a P-V diagram and calculate both the heat transfer and the total work.
Borgnakke Entropy of a liquid or a solid Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which this textbook has been adopted. It is now heated up to oC. Find the heat transfer and the entropy change using the steam tables. Repeat the calculation using constant heat capacity and incompressibility.
Constant pressure heating. Find the final temperature and the change in entropy of the steel? Both blocks, no external heat transfer, C from Table A. What is the final uniform temperature and change in stored entropy neglecting any heat loss and work? Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the process.
Now we get changes in u's instead of h's. Assume the milk has the property of liquid water and find the entropy generated in the cooling process. Jug of milk. Control mass at constant pressure. Continuity Eq. The total mass is now cooled to ambient temperature 30oC. How much heat transfer was taken out and what is the steel-water entropy change? Energty Eq. It heats from 15oC to 70oC as the computer is turned on.
How much did the entropy increase? An amount of liquid water at 15oC, kPa is added to the container so a final uniform temperature of the steel and the water becomes 75oC. Neglect any water that might evaporate during the process and any air in the container. How much water should be added and how much entropy was generated?
The steel and the water no external heat transfer nor any work. Now 2 L of hot oC oil is mixed into the pan. Neglect any work term and find the final temperature and the entropy generation. Solution: Since we have no information about the oil density, we assume the same for both from Table A. Hint: write the entropy balance equation for the control volume that is the combination of the rock bed and the heat engine.
Solution: nd To get the work we must integrate over the process or do the 2 law for a control volume around the whole setup out to T0 C.
Heat engine plus rock bed out to T0. W and QL goes out. The specific heats are in Tables A. Calculate the net entropy change for this process. Borgnakke Entropy of ideal gases Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which this textbook has been adopted.
Find the change in the specific entropy, using a the steam tables, b the ideal gas water Table A. Solution: a State 1: Table B. Find the entropy increase s2 - s1? What if it is from to K? This heat pump operates between reservoirs at K and K. At the beginning of the low-temperature heat addition, the pressure is 1 MPa. During this process the volume triples. Analyze each of the four processes in the cycle and determine a.
The pressure, volume, and temperature at each point b. Find the final pressure and volume using Table A. Assume a reversible, adiabatic process. So this is a constant s isentropic expansion process. From Eq. Find the final pressure and volume using constant heat capacity from Table A. It is now cooled down to K. Find the heat transfer and the change in entropy using ideal gas. Ideal gas, constant volume so there is no work. Calculate the heat transfer during the process and the change of entropy of the air.
Air, control mass. The bullet acts as a piston initially held by a trigger. The bullet is released so the air expands in an adiabatic process. If the pressure should be kPa as the bullet leaves the cylinder find the final volume and the work done by the air.
So we realize that one piece of information is needed to get state 2. What is the new temperature and how much work is required? The gas is compressed to 2. Calculate the final temperature and the work per unit mass, assuming a. Variable specific heat, Table A. Constant specific heat, value from Table A. Air, a control mass undergoing a reversible, adiabatic process. With two terms zero in the entropy equation we have a zero for the entropy change. What is the final pressure, the heat transfer and the change in entropy?
Hydrogen, control mass. They are now thermally connected to a reversible heat pump, which heats one and cools the other with no heat transfer to the surroundings. When one tank is heated to K the process stops. Find the final P, T in both tanks and the work input to the heat pump, assuming constant heat capacities.
The entropy equation Eq. Show the process on a T—s diagram. Calculate the final temperature and the net work per kilogram of helium. With ideal gas and constant specific heat this gives relation in Eq.
The isothermal process has work as Eq. You now press the plunger piston in while holding your thumb over the exit hole so that an air pressure of kPa is obtained. The outside atmosphere is at P0, T0. State assumptions about the process for each case.
Find the final volume and temperature for both cases. Air in pump. Assume that both cases result in a reversible process. State 1: P0, T0 State 2: kPa,? One piece of information must resolve the? The process is then a reversible isothermal compression. A valve on the tank is opened, and the pressure inside quickly drops to kPa, at which point the valve is closed. Assuming that the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass withdrawn during the process.
The piston is released, and just before the piston exits the end of the cylinder the pressure inside is kPa. If the cylinder is insulated, what is its length? How much work is done by the air inside? So one piece of information is needed for the? An electric current now passes through a resistor inside the tank. Is this possible? Borgnakke Polytropic processes Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which this textbook has been adopted.
Sketch the process in a P-v and a T-s diagram. Find the specific work and specific heat transfer in the process. Give the sign for the heat transfer and work terms and explain.
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