Question

2- 2.0 kg of nitrogen, as an ideal gas inside a piston-cylinder combination, performs a Carnot refrigeration cycle (closed system, i.e. no nitrogen leaves or enters the cylinder). The highest and the lowest temperature of the cycle are 177°C and 23°C, respectively. Work is added to the nitrogen (input work to the piston) in an adiabatic manner to increase the pressure of nitrogen to 4500 kPa. Label this process as 1-2. The pressure of nitrogen right after adiabatic expansion is 3000 kPa. Answer the following questions: a) Sketch this cycle on a P-v diagram (10 points) (Start from one point and follow the 4 isothermal and adiabatic processes necessary to form the Carnot cycle, the p-v diagram does not need to be scaled, just show the each point, each process and label them. Also show and label the adiabatic lines and constant temperature lines) b) Sketch this cycle on a T-s diagram (Label the pressures and the temperature lines and show the constant pressure lines) (10 points) c) Find work and heat transfer for each of the four processes (80 points) e) Determine the COP for this cycle (10 points) Answers: $W_{12}$?-230kJ, $Q_{12}$?0, $W_{23}$?-285kJ, $Q_{23}$?-285, $W_{34}$?230kJ, $Q_{34}$?0, $W_{41}$?185kJ, $Q_{41}$?185, COP?1.9)

          2- 2.0 kg of nitrogen, as an ideal gas inside a piston-cylinder combination, performs a Carnot refrigeration cycle (closed system, i.e. no nitrogen leaves or enters the cylinder). The highest and the lowest temperature of the cycle are 177°C and 23°C, respectively. Work is added to the nitrogen (input work to the piston) in an adiabatic manner to increase the pressure of nitrogen to 4500 kPa. Label this process as 1-2. The pressure of nitrogen right after adiabatic expansion is 3000 kPa. Answer the following questions:
a) Sketch this cycle on a P-v diagram (10 points)
(Start from one point and follow the 4 isothermal and adiabatic processes necessary to form the Carnot cycle, the p-v diagram does not need to be scaled, just show the each point, each process and label them. Also show and label the adiabatic lines and constant temperature lines)
b) Sketch this cycle on a T-s diagram (Label the pressures and the temperature lines and show the constant pressure lines) (10 points)
c) Find work and heat transfer for each of the four processes (80 points)
e) Determine the COP for this cycle (10 points)
Answers: $W_{12}$?-230kJ, $Q_{12}$?0, $W_{23}$?-285kJ, $Q_{23}$?-285, $W_{34}$?230kJ, $Q_{34}$?0, $W_{41}$?185kJ, $Q_{41}$?185, COP?1.9)

2- 2.0 kg of nitrogen, as an ideal gas inside a piston-cylinder combination, performs a Carnot refrigeration cycle (closed system, i.e. no nitrogen leaves or enters the cylinder). The highest and the lowest temperature of the cycle are 177°C and 23°C, respectively. Work is added to the nitrogen (input work to the piston) in an adiabatic manner to increase the pressure of nitrogen to 4500 kPa. Label this process as 1-2. The pressure of nitrogen right after adiabatic expansion is 3000 kPa. Answer the following questions:
a) Sketch this cycle on a P-v diagram (10 points)
(Start from one point and follow the 4 isothermal and adiabatic processes necessary to form the Carnot cycle, the p-v diagram does not need to be scaled, just show the each point, each process and label them. Also show and label the adiabatic lines and constant temperature lines)
b) Sketch this cycle on a T-s diagram (Label the pressures and the temperature lines and show the constant pressure lines) (10 points)
c) Find work and heat transfer for each of the four processes (80 points)
e) Determine the COP for this cycle (10 points)
Answers: W12?-230kJ, Q12?0, W23?-285kJ, Q23?-285, W34?230kJ, Q34?0, W41?185kJ, Q41?185, COP?1.9)

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