K23231 SUPPLEMENTARY PROBLEMS
For New Topics Introduced in the Eighth Edition of
“Thermodynamics and Heat Power” by Granet and Bluestein
Section 6.7 Steady Flow Gas Processes
S6.1 A compressor receives 40 m3/min of air at 300K and 101 kPa and discharges air at 430K
and 606 kPa. The heat rate out is 2.1 kW. Find the power required to drive the compressor and
the output flow rate . Assume an ideal gas and no changes of potential or kinetic energy.
Ans. 104.24 kW, 9.56 m/min
S6.2 Helium expands polytropically through a turbine at pV1.5 = C. Inlet is at 1000K and 1000
kPa. Exit is at 150 kPa. The turbine produces 105 kW. Find (a) exit temperature, (b) heat flow
rate, and (c) mass flow rate.
Ans. 531.33K, 16,704 kW, 34.25 kg/s
S6.3 One kg/s of CO2 flows through a device where p, v, and velocity are each tripled, per pvn =
C. Inlet p = 200 kPa, inlet specific volume is 0.4 m3/kg and inlet velocity is 100 m/s. Find (a) n,
(b) T1 and T2, (c) Δh, (d) power, and (e) heat transfer per kg.
Ans. n = -1, T1 = 423.28K, T2 = 3809.52K, Δh = 2866.11 kJ/s, power = -320 kJ/s, heat transfer =
2586.1 kJ/kg
S6.4 Nitrogen expands through a turbine in a reversible adiabatic process. Inlet T1 = 1100K and
p1 = 550 kPa. Outlet p2 = 100 kPa and the turbine produces 37 MW. Find (a) T2, (b) mass flow
rate, and (c) change in enthalpy.
Ans. 675.88K, 83.97 kg/s, -441.25 kJ/kg
S6.5 A turbine takes in 210 ft3/s of air at 100 psia and 1400oR and expands it to 14.7 psia
according to pV1.45 = C. Find the power and heat transfer rate, neglecting kinetic and potential
energy changes.
Ans. 7,131 hp, -486.7 Btu/s
Section 6.9 Frictional Effects
S6.6 One kg of CO2 in a constant pressure piston-cylinder is initially at 101 kPa and 417K. It
receives paddlework and rejects heat until it reaches 277K. Heat rejected is five times the work
input. Find (a) heat rejected, (b) paddlework, (c) change of enthalpy and (d) net work.
Ans. 132.3 kJ, 13.82 kJ, -118.5 kJ, -26.46 kJ
K23231 SUPPLEMENTARY PROBLEMS
p. 2
S6.7 Same problem as S6.6 except in this case the heat rejected is three times the paddlework
(i.e. Q = -3Wp). Find the paddlework and the change in internal energy.
Ans. 59.33 kJ, - 92.5 kJ
S6.8 One half pound of air expands in a piston cylinder from one ft3 to two ft3. Initial pressure is
100 psia. Thirty Btu of paddlework is added in this process. How much heat must be removed to
keep the air’s temperature constant and what is this temperature?
Ans. 17.17 Btu, 540oR
S6.9 An cylinder containing 0.2 kg of air with a 30 cm diameter piston receives 10 kJ of heat
which causes the piston to slide 30 cm under the expansion of the air. Initial volume is 0.2 m3.
Sliding friction adds 5 kJ to the air. Pressure is constant at 101 kPa. Find the initial and final air
temperatures and the work done.
Ans. T1 = 351.2K, T2 = 441.46K, 2.14 kJ
S6.10 A rigid tank, one m3, receives 500 kJ of heat plus 100 kJ of paddlework. The tank contains
steam originally at 300 kPa and 40% quality. Find the final steam temperature and quality.
Ans. 133.55oC, 47.35%
S.6.11 One kg of nitrogen is compressed from a volume of 0.5 m3 to 0.1 m3 at a constant
pressure of 200 kPa. Fifty kJ of heat plus 20 kJ of paddlework are added. Find the initial and
final temperatures of the nitrogen and the work done.
Ans. T1 = 336.93K, T2 = 538.7K, -80 kJ
Section 7.9 Air Conditioning
S7.1 What heat transfer rate is required to increase the dry bulb temperature of atmospheric air
initially flowing at 2000 cfm from 52oF to 89oF? If the relative humidity at 52oF is 70%, what is
the final relative humidity?
Ans. 1414.3 Btu/min, 20%
S7.2 Outdoor air at 40oF and ϕ = 90% enters a heater-humidifier to be heated to 75oF, then
humidified to 77oF and ϕ = 40%. Air flow rate is 2100 cfm. Find the heat rate required and the
water flow rate needed.
Ans. 1424.3 Btu/min, 0.52 lb/min
K23231 SUPPLEMENTARY PROBLEMS
p. 3
S7.3 Outdoor air at 10oC and ϕ = 30% is to be heated to 22oC then humidified to 25oC and ϕ =
60%. Air flow rate is 50 m3/min. Find the heating rate and the mass flow rate of water required.
Ans. 746.28 kJ/min, 0.603 kg/min
S 7.4 Atmospheric air enters an air conditioner at 30oC and 80% relative humidity at a rate of 12
m3/min. It leaves saturated at 20oC. Find the rate of cooling and the rate of moisture removal.
Ans. 371.8 kJ/min, 0.095 kg/min
S7.5 Atmospheric air at 90oF and ϕ = 80% is cooled, dehumidified and reheated to 70oF and
45% relative humidity. Find the heat removed in the cooler, the heat added in the reheater, and
the mass of water removed, all in per pound of dry air in the cooler.
Ans. 29.5 Btu/lb, 4.8 Btu/lb, 0.0175 lb/lb
S7.6 2,000 m3/min of outside air enters an air handler at 40oC and ϕ = 60%. Conditioned air
leaves at 7oC and ϕ = 80%. The dehumidified water removed is at 10oC. Find (a) mass flow rate
of the air, (b) rate of heat removal, and (c) rate of water removed.
Ans. 129,000 kg/hr, 1.2 x 107 kJ/hr, 3,030 kg/hr
Section 9.5 Automotive Engine Analysis
S9.1 A four stroke 6 cylinder Diesel engine with a bore of 10 cm and a stroke of 12 cm produces
120 kW running at 2500 rpm. Find the mean effective pressure.
Ans. 1,019 kPa
S.9.2 An air engine running on the Otto cycle has a compression ratio of 7.5. The engine uses
fuel with a heating value of 40,000 kJ/kg with an air/fuel ratio of 16. Find the thermal efficiency
of the cycle and the work done per kg of air.
Ans. 0.553, 1,382.5 kJ/kg
S9.3 An air engine produces an indicated power of 320 kW operating on an Otto cycle with a
compression ratio of eight. It uses 1 kg of fuel per minute with a heating value of 40,000 kJ/kg.
Frictional power is measured at 32 kW. Find (a) thermal efficiency, (b) theoretical power output,
(c) brake power output, (d) brake engine efficiency, and (e) indicated efficiency.
Ans. 0.565, 376.67 kW, 288 kW, 0.432, 0.48
K23231 SUPPLEMENTARY PROBLEMS
p. 4
S9.4 An auto engine with a thermal efficiency of 45% consumes fuel at a rate of 0.5 lbm/bhp-hr
when running at 3,000 rpm. The heating value of the fuel is 20,000 Btu/lbm. Brake power is
measured at 140 hp. Find the theoretical power output and the brake engine efficiency.
Ans. 212 hp, 0.297
S9.5 A six cylinder engine with a bore and stroke of 3.5 x 3.5 inches produces an indicated
power of 140 hp. Find the indicated mep if it runs at 3,000 rpm.
Ans. 182.9 psi
Section 11.8 Analysis of Fins
S11.1 Mild steel (k = 45 kW/oC) fins are to be attached to a vertical wall. Each fin is 20cm high,
1 cm thick and extends 10 cm from the wall. How man fins are required to remove 100 Watts
from the wall whose hc = 10 W/m2-oC and if the wall is at 75oC and the air at 20oC?
Ans. Five fins
S11.2 A flat hot plate is fitted with 10 fins to dissipate 100 Watts in a 60oF air stream. Each fin
is 6 inches high, 0.1 inch thick and 6 inches wide and is made of mild steel (k = 26 Btu/hr ft oF).
If hc = 1 Btu/hr ft2 oF, find the expected plate temperature.
Ans. 134.4 oF
S11.3 A transistor case in the shape of a vertical cylinder reaches 80oC when in air at 20oC. The
case is 1 cm high by 3 mm radius. Find the rate of heat loss to the air due to convection.
Ans. 0.141 W
S11.4 To improve heat loss, a thin aluminum sleeve with six symmetric projecting radial fins is
slipped over the transistor case of problem S11.3. Fins are 1 mm thick and extend 10 mm
outward. Find the new heat loss rate, neglecting radiation, and assuming the temperature of the
outer surface of the sleeve is at 80oC.
Ans. 1.037 W
S11.5 A thin flat plate 20 cm x 20 cm (hot side up) produces 50 Watts. Heat is to be transferred
from the plate entirely by vertical brass fins 10 cm high, 10 cm wide and 2 mm thick attached to
the plate. How many fins are needed to ensure the plate surface never exceeds 70oC when
exposed to 20oC air?
Ans. 11 fins
K23231 SUPPLEMENTARY PROBLEMS
p. 5
S11.6 If there is space for only one fin to remove heat from a vertical plate, is it better to have a
thick fin or a thin fin if the m value is to be maximized?
Ans. Thin fin