Thermodynamics I Spring 2014

Homework #3 Due 4/22 (Tue)

3.43 A piston/cylinder assembly contains 2 kg of liquid water at 20℃ and 300 kPa, as shown in

Fig. P3.43. There is a linear spring mounted on the piston such that when the water is heated,

the pressure reaches 3 MPa with a volume of 0.1 m3.

a. Find the final temperature.

b. Plot the process in a P-v diagram.

c. Find the work in the process.

3.47 A nitrogen gas goes through a polytropic process with n = 1.3 in a piston/cylinder. It starts out

at 600 K, 600 kPa, and ends at 800 K. Is the work positive, negative, or zero?

Thermodynamics I Spring 2014

3.59 Find the phase and the missing properties of P, T, v, u, and x for water at

a. 500 kPa, 100℃

b. 5000 kPa, u = 800 kJ/kg

c. 5000 kPa, v = 0.06 m3/kg

d. -6℃, v = 1 m3/kg

3.75 A rigid tank contains 0.5 kg of R-134a at 40℃, 500 kPa. The tank is placed in a refrigerator

that brings it to -20℃. Find the process heat transfer and show the process in a P-v diagram.

3.83 A piston/cylinder arrangement with a linear spring as shown in Fig. P3.83 contains R-134a at

15℃, x = 0.4 and a volume of 0.02 m3. It is heated to 60℃, at which point the specific

volume is 0.03002 m3/kg. Find the final pressure, the work, and the heat transfer in the

process.

Thermodynamics I Spring 2014

3.103 Nitrogen at 300 K, 3 MPa is heated to 500 K. Find the change in enthalpy using (a) Table

B.6, (b) table A.8, and (c) Table A.5.

3.111 A 10 m high cylinder, with a cross-sectional area of 0.1 m2, has a massless piston at the

bottom with water at 20℃ on top of it, as shown in Fig. P3.111. Air at 300 K, with a

volume of 0.3 m3, under the piston is heated so that the piston moves up, spilling the water

out over the side. Find the total heat transfer to the air when all the water has been pushed

out.

3.114 A constant-pressure piston/cylinder contains 0.5 kg air at 300 K, 400 kPa. Assume the

piston/cylinder has a total mass of 1 kg steel and is at the same temperature as the air at any

time. The system is now heated to 1600 K by heat transfer.

a. Find the heat transfer using constant specific heats for air.

b. Find the heat transfer not using constant specific heats for air.

Thermodynamics I Spring 2014

3.124 A piston/cylinder contains pure oxygen at ambient conditions 20℃, 100 kPa. The piston is

moved to a volume that is seven times smaller than the initial volume in a polytropic

process with exponent n = 1.25. Use the constant specific heat to find the final pressure and

temperature, the specific work, and the specific heat transfer.

3.126 An air pistol contains compressed air in a small cylinder, as shown in Fig. P3.126. Assume

that the volume is 1 cm3, the pressure is 1 MPa, and the temperature is 27℃ when armed. A

bullet, with m = 15 g, acts as a piston initially held by a pin (trigger); when released, the air

expands in an isothermal process (T = constant). If the air pressure is 0.1 MPa in the

cylinder as the bullet leaves the gun, find

a. the final volume and the mass of air

b. the work done by the air and the work done on the atmosphere

c. the work done to the bullet and the bullet exit velocity

3.131 A helium gas is heated at constant volume from 100 kPa, 300 K to 600 K. A following

process expands the gas at constant pressure to three times the initial volume. What is the

specific work and the specific heat transfer in the combined process?

Thermodynamics I Spring 2014

3.135 The piston/cylinder in Fig. P3.135 contains 0.1 kg R-410A at 600 kPa, 60℃. It is now

cooled, so the volume is reduced to half of the initial volume. The piston has upper stops

mounted, and the piston mass and gravitation are such that a floating pressure is 400 kPa.

a. Find the final temperature.

b. How much work is involved?

c. What is the heat transfer in the process?

d. Show the process path in a P-v diagram.