Air is compressed slowly in a piston-cylinder assembly from an initial state whe

Question

Air is compressed slowly in a piston-cylinder assembly from an initial state where p_1 = 20 lbf/in.^2, V_1 = 150 ft^3, to a final state where p_2 = 100 lbf/in.^2. During the process, the relation between pressure and volume follows pV = constant. For the air as the closed system, determine the work, in Btu. Carbon dioxide (CO_2) gas in a piton-cylinder assembly undergoes three processes in series that begin and end at the same state (a cycle). Expansion from State 1 where p_1 = 10 bar, V_1 = 1 m^3, to State 2 where V_2 = 4 m^3. During the process, pressure and volume are related by pV^1.5 = constant. Constant volume heating to State 3 where p_3 = 10 bar. Constant pressure compression to State 1. Sketch the processes on p-V coordinates and evaluate the work for each process, in kJ. What is net work for the cycle, in kJ? An electric motor operating at steady state draws a current of 20 amp at a voltage of 110 V. the output shaft rotates at a constant speed of 2000 RPM and exerts a torque of 9.07 N-m. Determine the input power, in W. the output power, in W. the cost of 24 hours of operation if electricity is valued at $0.09 per kW h. A 6-in. insulated frame wall of a house has an average thermal conductivity of 0.04 Btu/h middot ft middot degree R. The inner surface of the wall is at 68 degree F and the outer surface is at 40 degree F. Determine at steady state the rate of heat transfer through the wall, in Btu/h. If the wall is 20 ft Times 10 ft, determine the total amount of energy transfer in 10 hours, in Btu. Calculate the kinetic energy, in ft middot lbf, of an object whose mass is 20 lb moving with a velocity of 200 ft/s. The potential energy of an object of mass 90 kg is 44 kJ. For g = 9.81 m/s^2, determine the elevation relative to the Earth's surface, in m. An object of mass 15 kg is at an elevation of 100 m relative to the surface of the Earth. What is the potential energy of the object, in kJ? If the object were initially at rest, to what velocity, in m/s, would you have to accelerate it for the kinetic energy to have the same value as the potential energy you calculated above? The acceleration of gravity is 9.8 m/s^2. In a recent airline disaster, an airliner flying at 30,000 ft, 550 mi/h, lost power and fell to Earth. The mass of the aircraft was 255,000 lb. If the magnitude of the work done by drag force on the plane during the fall was 2.96 Times 10^6 Btu, estimate the velocity of the aircraft at the time of impact, in mi/h. Let g = 32.08 ft/s^2.

Explanation / Answer

a) mass m = 20 lb

speed v = 200 ft/s

KE = mv2/2 = 20*2002/2 = 400000 lb-ft2

b) mass m = 90 kg

PE = 44 kJ

g = 9.81 m/s2

PE = mgh

h = 44000/(90*9.81) = 49.84 m

mass m = 15 kg

height h = 100 m

PE = mgh = 15*9.81*100 = 14715 J

KE = PE = 14715 = mv2/2

v = sqrt(1475*2/15) = 44.29 m/s

final velocity = 44.29 m/s

the body needs to be accelerated to 44.29 m/s to have the same KE as equal to PE.

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