# Thermodynamic homeworks

Problem 1:

i. Check the applicability of the ideal gas modal for Refrigerant 134a at a temperature of 80C and a pressure of 1.6 Mpa.

ii. In what kind of pot will a given volume of water boil at a higher temperature: a tall and narrow one or a short and wide one? Explain.

iii. Saturated liquid water contained in a closed, rigid tank is cooled to a final state where the temperature is 50 degrees C and the masses of saturated vapor and liquid present are 0.03 and 1999.97 kg respectively. Determine the heat transfer for the process in kJ.

Problem 2:

Carbon dioxide, (CO2) gas, initially at 70 degrees F, 15 lbf/in2, and 1ft3, is compressed in a piston-cylinder assembly. During the process, the pressure and specific volume are related by pv1.2=constant. The amount of energy transfer to the gas by work is 45 Btu/lb of CO2. Determine the final temperature and the heat transfer in Btu/lb of gas.

Problem 3:

A cycle, composed of three processes: polytropic compression (n=1.5) from 137 kPa and 38 degrees C to state 2, constant pressure from state 2 to state 3, and constant volume from state 3 to state 1. The heat rejected is 1560 kJ/kg, and the substance is air. Determine:

a. The pressures, the temperatures, and specific volumes around the cycle

b. the heat added

c. the work for each process and the net work.

Problem 4:

A nitrogen line, 300 K and 0.5 Mpa, shown in the figure, is connected to a turbine that exhausts to a closed initially empty tank of 50m3. The turbine operates to a tank pressure of 0.5 Mpa, at which point the temperature is 250K. Assuming the entire process is adiabatic, determine the turbine work.

Problem 5:

i. An inventor claims to have developed a refrigeration system that removes heat from cooled region at -85C and transfers it to the surrounding air at 25C while maintaining a COP of 5.5. Is this claim reasonable? Why?

ii. In a steam power plant, 6000kg/s of steam enters the turbine at 8MPa, 480C, and expands to 0.7 Mpa. If the turbine has an efficiency of 90%, calculate the turbine net work in kW, the actual turbine exit temperature and entropy.

Problem 6:

i. It is desired to double the efficiency or a Carnot heat engine from 30% by raising its temperature of heat addition, while keeping the temperature of heat rejection constant. What percent increase in high temperature is required?

ii. A Carnot cycle engine using 1 kg air has the following conditions: heat addition beginning at 15 MPa and 1200 K and continuing until the pressure is 10 MPa; isothermal compression from 100kPa and 300 K and continuing until the pressure is 150 kPa. Determine:

a) the heat transfer into the cycle

b) the heat transfer from the cycle

c) the work for each of the processes

d) the cycle efficiency

Problem 7:

i. A process that violates the 2nd law of thermodynamics violates the first law.

_____True

_____False

ii. An experiment is being conducted on a new refrigerator design. During on test that lasts 1 hour, the following were made: 2.1 kW power consumed, 90000 kJ or heat removes from refrigerated space at temperature -23C, and a kitchen temperature of 300K. Are these measurements reasonable? Why?

iii. Calculate the thermal efficiency of a Carnot engine operating between 750C and 250C. What would be the COP of this device if it were reversed and run as a refrigerator? As a heat pump?

Problem 8:

i. A mass of 1 kg of air contained in a cylinder at 1.5 MPa, 1000K, expands in a reversible adiabatic process to 100kPa. Calculate the final temperature and the work done during the process, using: i) constant specific heats ii) variable specific heats

ii. Write the isentropic efficiency of each of the following devices in terms of the enthalpy, h.

Problem 9:

i. Calculate the thermal efficiency of a Carnot engine operating between 1500K and 300C.

ii. What would be the COP of the device in part (I) if it were reversed and run as a refrigerator? As a heat pump?

iii. Steam at 5.0 MPa, 500C enters an insulated turbine operating at steady state with a mass flow rate of 7kg/s and exits at 0.3 MPa. Kinetic and potential energy effects are negligible. Determine the maximum theoretical power that can be developed by the turbine, in kW, and the corresponding exit temperature. If the steam exits the turbine at 250C, and 0.5 MPa, determine the isentropic efficiency.

Problem 10:

i. It is desired to double the efficiency of a Carnot heat engine from 30% by raising its temperature of heat addition, while keeping the temperature of heat rejection constant. What percent increase in high temperature is required?

ii. The Novel Air Conditioning Company claims to have developed a new air conditioner, which will maintain a room at 22C while rejecting 105kJ of heat at 42C. The unit requires 10kJ or work. Is this device believable? Why?

iii. It is desired to calculate the mass of R 134a in 250 Liters tank at 1.5 MPa, 160C, and three different methods are suggested:

a) ideal gas equation

b) Refrigerant Tables

c) Generalized compressibility chart

d) Which is the most accurate method, and what percent differences are the other two?

Problem 11:

i. Which process requires more energy: completely vaporizing 1 kg of saturated liquid at 1-atm pressure or completely vaporizing 1 kg of saturated liquid at 8-atm pressure? Explain.

ii. Argon enters an insulated nozzle at 3.0 bars, 1200K, 10 m/s and exits at 1 bar, 800K. For steady state operation, determine i) the exit velocity, in m/s ii) the isentropic nozzle efficiency. (HINT: assume Argon an ideal gas).

iii. Two well-insulated tanks contain air. Initially, tank A hold 1.0 lb of air at 1440K, and tank B has 2.0 lb of air at some unspecified initial temperature. A valve in the line connecting the two tanks is opened and the contents are allowed to mix until equilibrium in attained at a temperature of 1080K. Assuming the ideal gas model, determine the initial temperature in tank B.

Problem 12:

i. A reversed Carnot engine as a heat pump consumes 6kW and has a COP of 3.0. A house containing 1800kg of air, is initially at 12C and the heat raises the air temperature to 21C. How long will this take?

ii. A heat pump is used for cooling in summer and heating in the winter. The house is maintained at 24C year-round. The heat loss is 0.44kW per degree difference between outside and inside temperatures. The average outside temperature is 32C in the summer and -4C in the winter. Determine:

i.) The power requirements for both heating and cooling.

ii.) Which condition determines the unit size that must be purchased?

iii. A steam power plant has steam leaving the boiler at 1MPa and 300C. If the plant operated with a condenser pressure of 20kPa, calculate the thermal efficiency and the net work output for the cycle.