ME 200 - HOMEWORK #9 – FALL 2014 9.1

ME 200 - HOMEWORK #9 – FALL 2014
DUE: WEDNESDAY, DECEMBER 3, 2014
9.1
Steam undergoes an isentropic compression in an insulated piston-cylinder assembly from an
initial state where T1 = 160oC, p1 = 3 bar to a final state where the pressure p2 = 160 bar.
Determine the final temperature, in oC, and the work, in kJ per kg of steam.
9.2
Steam enters a nozzle operating at steady state at p1 = 120 lbf/in.2 and T1 = 600oF with a velocity
of 85 ft/s. The pressure and temperature at the exit are p2 = 20 lbf/in.2 and T2 = 250oF. There is
no significant heat transfer between the nozzle and its surroundings, and changes in
potential energy between inlet and exit can be neglected. Determine the nozzle efficiency.
9.3
Carbon dioxide (CO2) at 1 bar, 300 K enters a compressor operating at steady state and is
compressed adiabatically to an exit state of 10 bar, 520 K. The CO2 is modeled as an ideal gas,
and kinetic and potential energy effects are negligible. For the compressor, determine:
(a) the work input, in kJ per kg of CO2 flowing
(b) the rate of entropy production, in kJ/K per kg of CO2 flowing
(c) the isentropic compressor efficiency
9.4
An air compressor operates at steady state with air entering at p1 = 2 bar, T1 = 35oC, and exiting at
p2 = 6 bar. Determine the work and heat transfer per unit of mass passing through the device, in
kJ/kg, if the air undergoes a polytropic process with n = 1.3. Neglect changes in kinetic and
potential energy between the inlet and the exit. Use the ideal gas model of air.
9.5
Liquid water at 70oF, 14.7 lbf/in.2 and a velocity of 30 ft/s enters a system at steady state
consisting of a pump and attached piping and exits at a point 30 ft above the inlet at 250 lbf/in.2,
a velocity of 15 ft/s. and no significant change in temperature. Let g = 32.2 ft/s2
(a) In the absence of internal irreversibilities, determine the power input required by the system,
in Btu per lb of liquid water flowing.
(b) For the same inlet and exit states, in the presence of friction would the power input be greater
or less than determined in part (a)? Explain.
9.6
Consider the turbocharger arrangement shown below in which a turbine generates power to drive
a compressor. Air enters the turbine at 4500C and 135 kPa and flow rate of 0.02 kg/s and leaves
the turbine at 4000C and 95 kPa. Air enters the compressor at 700C and 95 kPa at a rate of 0.018
kg/s and leaves at 135 kPa. The mechanical efficiency between the turbine and compressor is
95% (i.e. 5% of the turbine work is lost during transmission to the compressor). Determine
(a) the air temperature at the compressor exit (K),
(b) the isentropic efficiency of the turbine (%), and
(c) the isentropic efficiency of the compressor (%).
Turbine
Compressor