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Modern Engineering Thermodynamics

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162 CHAPTER 5: First Law Closed System Applications<br />

Assume the room air is at 14.7 psia and 70.0°F during the entire<br />

process.<br />

13.* The human body under the stress of exercise can release 230. W<br />

as heat. Assume the human body to be a closed system and<br />

neglect any work or change in kinetic energy. Determine the rate<br />

of change in internal energy of the human body as a 68.0 kg<br />

person runs at a constant velocity up a staircase having a vertical<br />

height of 15.0 m in 60.0 s.<br />

14.* Exactly 14.0 kg of herpes duplex virus scum is compressed<br />

from a volume of 4.50 to 1.50 m 3 in a process where p is in<br />

N/m 2 is given by p = 60:0/V + 30:0, when V is in m 3 . During<br />

the compression process the virus gives off 20.0 J of heat and<br />

turns a putrid yellow in color. Determine the change in the<br />

specific internal energy of the virus for this process.<br />

15.* Exactly 3.70 kg of nitrogen gas at exactly 0°C and 0.100 MPa is<br />

put into a cylinder with a piston and compressed in a process<br />

defined by pV 2 = constant. When the final pressure in the<br />

cylinder reaches 10.0 MPa, and assuming ideal gas behavior,<br />

determine (a) the amount of work done on the nitrogen by the<br />

piston and (b) the final temperature of the nitrogen.<br />

16. Heat is transferred to 0.100 lbm of air contained in a frictionless<br />

piston-cylinder apparatus until its volume expands from an<br />

initial value of 1.00 ft 3 to a final value of 1.50 ft 3 . Calculate the<br />

work transport of energy and the heat transfer when the system<br />

is the air in the cylinder. The initial temperature of the air is<br />

70.0°F. Consider air to be an ideal gas.<br />

17. Exactly 0.100 lbm of air (an ideal gas) initially at 50.0 psia and<br />

100.°F in a cylinder with a movable piston undergoes the<br />

following two-part process. First, the air is expanded<br />

adiabatically to 30.0 psia and 24.0°F, then it is compressed<br />

isobarically (i.e., at constant pressure) to half its initial volume.<br />

Determine<br />

a. The final temperature at the end of the isobaric compression.<br />

b. The work produced during the adiabatic expansion.<br />

c. The heat transfer during the isobaric compression.<br />

18.* A 1000. kg battery powered adiabatic electric vehicle has a fully<br />

charged battery containing 20.0 MJ of stored energy. If it<br />

requires 12.0 kW of power to keep it moving at a constant<br />

velocity on a horizontal road, determine how long the vehicle<br />

will operate before its battery is fully discharged.<br />

19. How many watt hours of electricity are needed to heat the<br />

contents of a sealed, rigid, insulated chamber pot containing<br />

0.300 lbm of water from 50.0°F with a quality of 1.00% to a<br />

saturated vapor. The chamber pot has an internal electrical<br />

resistance heater with a power cord that plugs into a standard<br />

110. V ac outlet.<br />

20.* A small, sealed, rigid container holding 0.500 kg of water is<br />

heated in a microwave oven drawing 1600. W at 2460 MHz.<br />

The oven’s timer is set for exactly 1 min. The initial<br />

thermodynamic state of the water is 20.0°C at 1.00 atm. After<br />

the 1 min heating period, determine (a) the water’s work<br />

transport of energy, (b) the water’s heat transport of energy,<br />

(c) the change in specific internal energy of the water, and (d) the<br />

final temperature and pressure assuming the liquid water to be<br />

an incompressible liquid with a specific heat of 4.50 kJ/(kg·K).<br />

21.* 30.5 kg of H 2 O contained in a 1.00 m 3 rigid tank are at an<br />

initial pressure of 10.0 MPa. The contents of the tank are cooled<br />

at constant volume until a final pressure of 2.00 MPa is reached.<br />

Determine the final temperature, the final value of the specific<br />

internal energy, and the process heat transfer.<br />

22. A small rigid tank 1.00 ft 3 in volume contains saturated water<br />

vapor at 300.°F. An initially evacuated rigid container 3.4549 ft 3<br />

in volume is then attached to the first tank and the<br />

interconnecting valve is opened. The combined system is then<br />

brought to equilibrium at 300.°F by an appropriate heat<br />

transport of energy. Determine the final pressure in the system<br />

and the required heat transfer.<br />

23. A pressure vessel that has a volume of 0.200 ft 3 is filled with<br />

saturated liquid Refrigerant-22 at 70.0°F. An evacuated container<br />

4.00 ft 3 in volume is attached to the vessel and the<br />

interconnecting valve is opened. The combined system is then<br />

brought to equilibrium at 70.0°F Calculate the heat transport of<br />

energy to (or from) the system.<br />

24.* A mixture of hydrazine and cow manure happens to have the<br />

same thermodynamic properties as pure water. A secret process<br />

requires that this mixture be vaporized then injected into light<br />

bulbs. Determine the work and heat transport of energy that<br />

occurs when 1.30 kg of this mixture is isothermally converted<br />

from a saturated liquid to a saturated vapor at 40.0°C.<br />

25. A lead bullet weighing 0.0200 lbf and traveling horizontally at<br />

3000. ft/s is suddenly stopped by a perfectly rigid object that<br />

does not deform during the impact. Find the temperature rise of<br />

the bullet assuming the impact occurs so rapidly that the impact<br />

process can be considered to be adiabatic. For lead, use<br />

Δu = 0.0130(ΔT) in Btu/lbm, where T is in °F orR.<br />

26. As a bullet travels down the barrel of a pistol, the pressure from<br />

the burning propellant behind it increases linearly with the<br />

volume V displaced by the bullet as p = V × 10 3 in psia, where V<br />

is in in. 3 . The total volume of the barrel is πR 2 L, where R is the<br />

radius of the bore and L is its total length. Determine the velocity<br />

of the bullet at the end of the barrel if it travels horizontally and<br />

adiabatically down the barrel without changing its internal<br />

energy and with no friction.<br />

Data<br />

Barrel length = 6.00 in<br />

Barrel diameter = 0.380 in<br />

Bullet mass = 5.00 g<br />

27. A rubber band weighing 1.00 × 10 –3 lbf that obeys Hooke’s law<br />

of elasticity is stretched horizontally and adiabatically from an<br />

initial length of 3.00 to 4.00 in.<br />

a. Determine the change in total internal energy of the rubber<br />

band when it is stretched, if its elastic modulus is 1.00 ×<br />

10 3 lbf/in 2 and its cross-sectional area remains approximately<br />

constant at 7.80 × 10 –3 in 2 .<br />

b. If the stretched rubber band is suddenly released horizontally<br />

and adiabatically, determine its final velocity neglecting air<br />

friction and any height change during its flight.<br />

28. A thin glass sphere 0.0250 ft 3 in volume is completely filled<br />

with 1.00 lbm of saturated liquid nitrogen. The glass sphere is<br />

sealed inside a large rigid, evacuated, insulated container whose<br />

volume is 10.0 ft 3 . What are the final pressure and quality<br />

(if any) inside the larger container if the glass sphere breaks.<br />

29. 1.00 ft 3 of saturated liquid water at 14.7 psia is poured into an<br />

initially evacuated, rigid, insulated vessel whose volume is 100. ft 3 .<br />

Inside the vessel is an electric heater that draws an effective 10.0 A<br />

at an effective 110. V. Once this heater is turned on, how long will<br />

it take the contents of the vessel to reach 40.0 psia?<br />

30.* A rigid vessel having a volume of 3.00 m 3 initially contains steam<br />

at 0.400 MPa and a quality of 40.2%. If 23.79 MJ of heat is added<br />

to the steam, determine its final pressure and temperature.

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