MEC11004 Thermodynamics Tutorial Booklet
Welcome to the MEC11004 Course.
These tutorials are here to help you understand the Thermodynamics course. The reasons we do tutorials are many, but the mains ones are a) it allows us to give you feedback b) it allows you to judge if you understand the course c) they can give you some confidence before going into the exam.
The tutorials are only here to help, we will not judge you on these, they do not form. part of any assessment.
If you can do the tutorials, without looking at the answers, you will be able to do the exam. If you can do all the questions without looking at the answers, I would expect you to get above 80% in the exam. I am telling you this because I know many of you see the exam mark and your final degree grade as the most important thing. I personally would like you to do the tutorials because you find it rewarding. I always enjoyed doing problem classes, but then academics are just a bit weird.
(See Thermo Lecture 1: Why academics are a bit weird.)
Also, the week 4 and week 8 tests are based on these questions.
As a bit of light relief, I’m using the Microsoft word colouring book to number the tutorials. The idea is you can print the page off and colour it in. (No, it is not for marks, there is no prize for the best colouring in, which is a shame, perhaps there should be?).
The plan is that the tutorials are organised by lecture week. If you have a tutorial in thermodynamics in week 1 then you should do the week 1 material. If your tutorial is week 3 you should have worked through weeks 1, & 2, but not week 3. The idea is you do the tutorial work weekly, along with the lectures, even if you have no thermodynamics tutorial that week. I know this can lead to frustration, when you cannot get a question done, so please keep an eye on the discussion board on Blackboard. If you are struggling have a look there, you can ask questions anonymously and there are separate pages for the different tutorials so you can quickly find the information. If you are posting a question, can you please put the question on the right tutorial page. Also but as a last resort the solutions are at the back of this booklet.
The new format might take a little getting used to, but we think it will help your learning. If you experience and difficulties with the new format then please drop me an email, [email protected] I will see what we can do. Please remember we are here to help. The reason we are taking a register is so that I can email and ask if you need more support. This information will not be stored, group tutorial attendance for MEC11004 will not form. part of your attendance record. [This may not be the case for other courses, but I do not get to decide that.]
You will need your Little Book of Thermofluids for the group tutorials.
MEC 11004 Thermodynamics Tutorial 1 Week 1
1) Convert: a). 540 L (litres) to m3 ; b). 4.5 bar to kPa ; c). 2 km to mm d). 12 km3 to litres
2) A balloon filled with helium initially at 1 bar and 25°C, is released and it rises to a height of 10km, the top of the troposphere, where the pressure is 0.2 bar and the temperature is 53°C (minus 53°C).
a) What is the ratio of the final to the initial volume, V2/V1?
[369%]
3) On a cool dry day in Sheffield the air temperature and pressure are 10°C and 1bar respectively.
a) Calculate the density of the air.
[1.23 kgm-3]
4) A high pressure 244 cu. ft cylinder is filled with air at 300 bar and 20°C. (1 cu. ft = 1 cubic foot, 1 ft = 12 inches; 1 inch = 25.4 mm)
a) What is the volume of the cylinder in m3?
b) What is the mass of the gas inside the cylinder?
c) 750 kg is allowed to rapidly escape from the cylinder, this cools the cylinder to 5°C.
(i) What is the pressure in the cylinder now?
[6.91 m3 ; 2465 kg ; 198 bar]
5) Define the following, giving an example of each.
a) Intensive property
b) Extensive properties
c) Specific properties,
6) Define the following properties and specify their units and if they are intensive or extensive properties.
a) internal energy,
b) enthalpy,
c) specific volume.
7) My kettle runs on a voltage of 240V and draws a current of 13A.
a) How long would it require to heat a cup of water (0.25L) from 10 to 100°C? You can assume no heat is lost through the walls of the kettle, i.e. they are adiabatic.
b) Electricity currently costs 34p per kWhr, how much does this cost?
c) If my kettle holds 1.74 kg of water, how much would it cost if you filled it and boiled it every time you wanted a single cup of tea?
d) How long would this take? [30.2 s; 0.89p ; 6.19p ; 3 min 29 s]
MEC 11004 Thermodynamics Tutorial 2 Week 2
1. In relation to thermodynamics:
a. What is meant by “the phase” of a system?
b. What is meant by “the state” of a system?
2. Define a) thermodynamic equilibrium, b) isothermal process.
3. Air cylinder of volume, 0.5 m3 at 25 °C and a pressure of 300 bar is heated by electric heater. The heater rapidly adds 2000 kJ of energy to the air.
a. Draw a diagram of the problem and the control volume.
b. Is your control volume, open, closed or isolated?
c. Calculate the final pressure if the cylinder does not expand.
[316 bar]
4. The cylinder on an engine is 300mm in diameter. The initial length of the cylinder is 100mm and its initial temperature is 200°C. The final length of the cylinder is 600mm.
a. If the connecting rod produces a constant force of 50 kN on the piston, how much work is done? [25 kJ]
5. A sealed box with fixed adiabatic walls 1m x 1m x 1m contains dry air at 0°C and 100 kPa. A battery powered electric heater within the box, rapidly supplies 1kJ of heat to the air in the box. Assuming no heat is lost.
a. Calculate the temperature of the air in the box, just after the heat is added, assuming the box does not expand.
b. If the box was instead allowed to expand, against the atmosphere as the air was heated, calculate the change in temperature and the work done.
[1.09 °C ; 0.78°C ; 0.287 kJ]
6. A perfectly insulated piston-cylinder device with an initial volume of 500 litres is filled with air at atmospheric pressure and 20°C. The outside of the cylinder is maintained at atmospheric pressure. The air is stirred by a paddle wheel whose work amounts to 30 kJ; while the air is heated by constant current of 8 A at 240V that flows for 45 seconds through a resistor placed in the air.
a. Draw a suitable diagram and define the control volume.
b. Determine the total change in internal energy of the air if the piston does not move.
c. Calculate the final temperature of the air.
i. If the piston does not move.
ii. If the piston is allowed to move.
[116.4 kJ ; 565 K ; 487 K]
MEC 11004 Thermodynamics Tutorial 3 Week 3
1) A piston cylinder device contains 0.75 kg of air at 10°C and a pressure of 1 bar. The air is compressed until the pressure is 10 bar. Assuming the process is polytropic with a polytropic constant of 1.4, calculate.
a) Draw a diagram of the system and the control volume.
b) The initial volume of the cylinder.
c) The final volume of the cylinder.
d) The work done.
[0.609 m3 ; 0.118 m3 ; -143 kJ]
2) A piston-cylinder device is part of an internal combustion engine. 0.5L of air and fuel mixture is taken into the cylinder and compressed to 1/10 of the original volume. (This is termed a compression ratio of 10:1).
At this point the fuel air mixture is ignited, and the temperature rises to 2000°C and the pressure to 50 bar. Assuming the polytropic constant for this process is 1.30; cv is 1.4 kJ kg-1 K-1 and cp is 1.68 kJ kg-1 K-1.
a) Draw a diagram of the system and the control volume.
b) Assuming that the fuel-air mixture can be treated as air, what is the mass of air in the cylinder?
c) The piston then moves down expanding the gas by a factor of 10, find the final temperature and pressure in the cylinder.
d) How much work has been done, what is the heat input?
e) If the engine is turning at 3000 RPM (revolutions per minute), and each of the 4 cylinders fires every two revolutions, how much power does the engine produce?
[3.83x10-4 kg ; 866°C, 2.51 bar ; 0.415 kJ, -0.1930 kJ ; 41.5 kW (56.4 HP)]
3) A bullet is fired from a gun. The bullet and the barrel can be treated as a polytropic piston cylinder device. The barrel is 1.0 metre long, has an inside diameter of 12.5 mm and an outside diameter of 25 mm. The charge initially takes up 50 mm of the barrel. Immediately after the ignition, the charge turns to gas at 400 bar and 2000°C. Assuming, the polytropic constant for this process is 1.5, that cV is 0.9903 kJ kg-1K-1 and cp is 1.198 kJ kg 1K-1 and that the molar mass M of the gas is 40 kg/kmol.
a) Draw a diagram of the system and the control volume.
b) Determine the initial volume and the final volume of the gas just before the bullet leaves the gun.
c) What is the temperature and pressure in the barrel as the bullet leaves it?
d) How much work is done on the bullet?
e) If the bullet is spherical, and made of lead (density 11,300 kg m-3), and all of the work done by the gas goes into accelerating it, how fast is it going as it leaves the barrel?
f) How much heat is transferred to the steel barrel, that has a density, r , 7,840 kg m-3, and specific heat, cV 0.45 kJ kg-1 K-1?
g) If the heat were evenly distributed, what is the temperature rise in the barrel?
[6.14´10-6 m3; 123´10-6 m3 ; 235°C, 4.47 bar ; 381 J ; 257 m s-1 ; -527 J ; 0.41°C]
MEC 11004 Thermodynamics Tutorial 4 Week 4
1) A 50kg block of stainless steel at 500K is dropped into a lake that is at 278K.
a) Calculate the change in entropy as the block cools to the temperature of the lake.
b) Calculate the heat transferred from the block to the lake.
c) Calculate the change in entropy of the system.
[-14.13 kJK-1 ; 5344 kJ ; 5.09 kJK-1]
2) One side of a wall in a house is maintained at 20°C while the outside is at 3°C. If 500W of heat is transferred across the wall.
a) What is the entropy generated at the warm side?
b) What is the entropy generated at the cold side?
c) What is the entropy generated by the wall?
[1.706 kJK-1 ; 1.812 kJK-1 ; 0.106 kJK-1]
3) An isentropic compressor takes in air at 0°C and 1 bar and compresses it to 25 bar. The mass flow rate is 1.75 kgs-1and the polytropic constant is 1.4.
a) Determine the output temperature.
b) Determine the power required by the compressor.
c) If the system was isothermal, what power, , (per kg) is required now?
[685 K ; -749 kW (cp 1.039 kJkg-1K-1) {or -741kW (1.028) or -725kW ( 1.006) or -775 kW (1.075) } ;
-441 kW]
4) Air enters a turbine at 1250°C and 30 bar, work is extracted, and it exits at 120°C. Assume the polytropic constant n =1.4 and cp =1.112 kJkg-1K-1
a) Assuming the turbine is isentropic what is the exit pressure?
b) What is the specific power of this turbine?
[0.26 bar ; 1257 kWkg-1]
5) Air at 500°C and 15 bar enters an isentropic turbine at a rate of 0.3 kg s 1. It leaves at a pressure of 1 bar.
a) At what temperature does the air leave the turbine? (Use relevant air properties at 600K see LBoT).
b) What is the power output of the turbine?
c) If the turbine has an isentropic efficiency of 80%, what is the power output of the turbine?
d) At what temperature does the air leave the turbine if it has this isentropic efficiency?
e) Show both processes on a T-s diagram.
[95.6°C ; 127.4 kW ; 102.0 kW ; 177 °C]
MEC 11004 Thermodynamics Tutorial 5 Week 5
1) Air at 200°C and 7.0 bar enters an isentropic diffuser at a flow rate of 0.005 kg s-1. The diffuser has an entrance cross sectional area of 5 mm2. If the exit is assumed to be very large and there is no heat loss; from the data in the LBOT page 39; determine.
a) An appropriate value for cp at the entrance. You may assume cp does not vary with pressure.
b) A suitable value for n, the polytropic constant.
c) Calculate the temperature and pressure at the outlet.
d) How would the final temperature and pressure differ if the isentropic efficiency were less than one?
[1.025 kJ/(kgK) ; 1.39 ; 218°C, 8 bar]
2) A 2 kg block of iron is heated to 500°C and suspended in a rigid, sealed insulated box containing 0.1 kg of air at 25°C and 1 bar. (Use properties for air at 500 K. The specific heat capacity for iron at these temperatures can be treated as 0.452 kJ kg-1 K 1 .)
a) What temperature will both ultimately become?
b) How much energy is transferred?
c) What are the entropy changes for each of the substances?
d) What is the total entropy change?
[464°C ; 32.5 kJ ; air 0.0673 kJ K-1, iron -0.0432 kJ K-1 ; 0.0240 kJ K-1]
3) A shower mixing head takes hot water at 65 °C and mixes it with cold water at 5 °C. If the desired temperature from the shower is 45 °C, what is the ratio of the hot and cold mass flow rates?
[2:1]
4) Air is heated by the output gases from a furnace. The air enters the heat exchanger at 95 kPa and 20 °C at a rate of 0.6 m3s-1. The gas from the furnace exits at 160 °C, at rate of 0.95 kgs-1 and 95 °C.
For Air cp=1.005 kJ/(kgK); For the exhaust gas cp = 1.10 kJ/(Kg/K)
a) What is the mass flow rate of the input gas?
b) Determine the rate of heat transfer.
c) Calculate the outlet temperature of the air.
[0.68 kgs-1 ; 67.9 kJs-1 ; 120 °C]
MEC 11004 Thermodynamics Tutorial 6 Week 6
1. A car engine with a power output of 90 kW has a thermal efficiency of 28%.
a. Determine the rate of fuel consumption at full power if the heating value of the fuel is 44,000 kJ kg 1
[26.3 kg/hour]
2. A heat engine runs between a source at 450°C and the atmosphere at 10°C.
a. What is its maximum possible efficiency?
b. Is this likely to be achieved?
[61%]
3. An inventor claims that his new design of heat engine takes 5 kW of heat from a 500°C source and produces 3 kW of power. If the sink temperature of the cycle is 60°C, are his claims plausible?
4. An ideal Brayton cycle uses a flow rate of 40 kg of air per second which enters the compressor at 1 bar and 20 °C. The turbine inlet temperature is 1200 °C. The compressor outlet pressure is at 18 bar. Use n = g =1.40 and cp = 1.005 kJ kg-1 K-1.
a. What is its outlet temperature of the compressor?
b. How much power does the compressor require?
c. What is its outlet temperature of the turbine?
d. How much power does the turbine produce?
e. What is the total power output of this cycle?
f. What is the heat input rate?
g. What is the efficiency of the cycle?
[396 °C ; -15.1 MW ; 372 °C ; 33.3 MW ; 18.1 MW ; 32.3 MW ; 56%]
5. A ground-based gas turbine for power production uses a Brayton cycle with a flow rate of 210 kg of air per second. The cycle will run with a turbine inlet temperature of 1145 °C and a compressor using atmospheric air with an inlet temperature of 10 °C. The compressor outlet pressure is 15 bar. The isentropic efficiency of both turbine and compressor is 87%. Use n = g =1.40 and cp = 1.005 kJ kg-1 K-1.
a. What is its outlet temperature of the compressor?
b. How much power does the compressor require?
c. How much power does the turbine produce?
d. What is its outlet temperature of the turbine?
e. What is the heat input rate?
f. What is the total power output of this cycle?
g. What is the efficiency of the cycle?
[340 °C ; -80 MW ; 140 MW ; 454 °C ; 160 MW ; 60 MW ; 37.5% ]
6. Cruising at altitude, a turbofan engine uses a Brayton cycle with a flow rate of 60 kgs-1. The turbine inlet temperature is 840 °C and the compressor air inlet temperature and pressure are -5 °C and 0.5 bar respectively. The pressure ratio across the compressor is 23. The pressure drop across the combustor is 6% of the pressure rise in the compressor. The isentropic efficiency of both turbine and compressor is 91%. Use n = g =1.40 and cp = 1.005 kJ kg-1 K-1.
a. What is its outlet temperature of the compressor?
b. How much power does the compressor require?
c. What is its outlet temperature of the turbine?
d. How much power does the turbine produce?
e. What is the total power output of this engine?
f. What is the heat input rate?
g. What is the efficiency of the cycle?
[421 °C ; -25.7 MW ; 249 °C ; -35.6 MW ; 9.9 MW ; 25.2 MW ; 39%]
7. A military jet aircraft is stationary at full throttle on the runway. Its jet engine uses a Brayton cycle. The ambient pressure and temperature are 1 bar and 10 °C respectively. The compressor has a pressure ratio of 23 and an isentropic efficiency of 91%. The pressure drop through the combustor is 2 Bar. The turbine inlet temperature is 1120 °C. The turbine, whose isentropic efficiency is 87%, is matched to the compressor and produces just enough power for the compressor’s requirements. The air flow rate is 50 kg per second. All of the air is exhausted through a nozzle whose isentropic efficiency is 90%. Use n = g =1.40 and cp = 1.005 kJ kg-1 K-1. Treat the fluid as air throughout.
a. What is the outlet temperature of the compressor?
b. How much power does the compressor require?
c. What is the heat input rate for this cycle?
d. What are the outlet temperature and pressure of the turbine?
e. At what temperature does the air come out of the nozzle?
f. How fast is the air going?
g. If the thrust in Newtons is equal to , what is the thrust rating of this engine? Assume that the inlet velocity is zero.
[461 °C ; 22.6 MW ; 33.1 MW ; 669 °C, 4.12 bar ; 387°C ; 753 m s-1 ; 37.7 kN]