(1) At the beginning of the compression, the air in an Otto cycle has a pressure and temperature of 100 kPa, 300 K. The maximum cycle temperature is 1000 K and the compression ratio is 8. Answer the following questions about this cycle using the cold air standard analysis assumptions and assuming all processes are ideal.
A. What is the temperature of the air after being compressed?
a. 426 K
b. 689 K
c. 732 K
d. 828 K
B. What is the air temperature at the end of the expansion?
a. 392 K
b. 435 K
c. 491 K
d. 632 K
C. How much heat is added to this system?
a. 192 kJ/kg
b. 223 kJ/kg
c. 294 kJ/kg
d. 312 kJ/kg
D. How much net work does this cycle produce?
a. 82 kJ/kg
b. 95 kJ/kg
c. 126 kJ/kg
d. 228 kJ/kg
E. What is the thermal efficiency of this cycle?
a. 20%
b. 32%
c. 42%
d. 56%
(2) Air is expanded from 800 kPa, 427 °C to 100 kPa through a reversible, steady-flow turbine. The process experienced by the air as it passes through the turbine is claimed to be one in which Pv13 remains constant. The turbine surroundings maintain their temperature at 27 °C as they exchange heat with the turbine. Assuming this claim is valid:
A. What is the temperature of the air at the turbine exit?
1. -37 °C
2. 53 °C
3. 77 °C
4. 160 °C
B. What is the ratio of voutiet to
1. 8.00
2. 4.95
3. 4.42
4. 3.81
C. How much heat is transferred between the turbine and its surroundings?
1. -50.8 kJ/kg
2. -35.1 kJ/kg
3. 35.1 kJ/kg
4. 63.7 kJ/kg
D. What is the change in the entropy of the air as it passes through this turbine?
1. 0 kJ/kg-K
2. -0.0562 kJ/kg-K
3. -0.0998 kJ/kg-K
4. 0.1140 kJ/kg-K
E. Is this claim valid?
1. yes
2. no
(3) Answer the following questions.
A. An adiabatic turbine operates with superheated steam at 4 MPa, 400 °C at its inlet and 70 kPa at its outlet. What is the minimum allowable water specific entropy at the turbine outlet?
B. Sketch P-v state diagram for a phase changing substance below. Sketch an isothermal process that extends from a subcooled liquid state to a superheated vapor state. Indicate on this diagram the reversible work produced by a steady-state, single-stream, internally reversible system undergoing this process.
C. A Camot heat engine operates with a 327 °C heat source and a 27 °C heat sink. How much work does this engine produce when 100 kJ of heat are transferred into it from the heat source?
D. (5 pts) Nozzles do not transfer
Or . (2 items)
E. (5 pts) Entropy is defined by:
e. ds = du /
f. ds = Sq /Tim,
g. ds = (du / T) +(Pdv T) a. the chaos of the universe
F. (5 pts) Write the equation for the change in the specific entropy of an ideal gas undergoing an isobaric process below.
G. (S pts) The only two forms of energy transfer associated with a closed system are and
(4) An inventor claims to have invented a heat engine that operates using energy reservoirs whose temperatures are 600 K and a 300 K. She also claims that this engine produces 10 kW of power while rejecting heat at a rate of 2 kW.
A. What is the rate at which heat is being transferred from the high-temperature reservoir to this heat engine?
1. 0 kW
2. 8 kW
3. 10 kW
4. 12 kW
B. What is the rate at which the entropy of the low-temperature reservoir is changing?
1. -24 kJ/hr-K
2. -12 kJ/hr-K
3. 12 kJ/hr-K
4. 24 kJ/hr-K
C. What is the rate at which the work production is changing the entropy of the engine surroundings?
1. -12 kJihr-K
2. 0 kJ/hr-K
3. 12 kJ/hr-K
4. 24 kJ/hr-K
D. What is the rate at which the entropy of the hot-reservoir changes?
1. -72 kJ/hr-K
2. -48 kJ/hr-K
3. 48 kJ/FINK
4. 72 kJ/hr-K
E. Does this system satisfy the second law?
1. yes
2. no
(5) A solar powered Rankine cycle as shown here uses water as its working fluid, operates its boiler at 4 MPa, and its condenser at 50 kPa. The temperature of the steam entering the turbine is 350°C. The turbine is sized to produce 300 MW of power. Answer the following questions assuming ideal operating conditions. Don't interpolate the tables, use the closest values instead. What is the mass flow rate through the boiler and the thermal efficiency of this cycle? This is a complete work-out problem requiring the full "System, Sketches including state diagrams, Conditions, Physical Laws, Properties, and Calculations" format of the course syllabus. Submit your answers below.