Exam #3 Spring 2000

1. A compressed ideal gas ( Cp = 1.0035 kJ/kg/ oC, Cv = .7165 kJ/kg/ oC) that has a mass of 2.80 grams at a temperature of 180 oC, a pressure of 790 kPa, and a volume of 5.90 liters is allowed to expand.

(A) If the expansion is carried out at a constant pressure until the gas's internal energy has increased by 280 J, What is the gas’s final temperature?
Ans:{320 oC}

(B) If the expansion is carried out at a constant temperature until the gas's final pressure is 35.9 kPa, how much heat does the gas absorb or lose during this process?
Ans:{14.4 kJ, absorbed}
(C) If the expansion is carried out in such away that there is no heat loss during the expansion process and the gas's final volume is 130 liters, how much work does the gas accomplish during this expansion process?
Ans:{8.26 kJ}
2. An equal amount of ice and water are mixed together in an insulated tank. The ice is initially at 0 0C and the water is at 65.0 oC.
(A) What is the final temperature of the mixture? Prove your answer.
Ans:{0.00 oC}
(B) What fraction of the total mass in the container is water when the system comes to equilibrium?
Ans:{90.8%}

(C) If it takes 6.12 kcal of heat energy to raise the temperature of the final mixture in the tank back up to 65.0oC how much mass was initially water?
Ans:{423 g}
3. A well-insulated box contains 380 kg of ice at 0 oC. A tube with a uniform radius of 2.30 cm passes through the box caring water that enters at 88.0 oC and exits at 74.0 oC. The water flows through the tube at the rate of 1.50 liters per second.
(A) What is the mass of the water that flows through the tube each second?
Ans:{1.50 kg/s}

(B) How long will it take to melt all the ice in the box if the exit temperature of the water remains constant at 74.0 oC until all the ice melts?
Ans:{24.0 min}

(C) How many joules of energy flowed from the water running through the tube into the ice that becomes water in the box when the exit temperature of the water in the tube is 88.0 oC - the same as the temperature at which it enters the box?
Ans:{267 MJ}

4. An ideal gas ( cp = 12.744 cal/mole/K) is heated and compressed from an initial state at a temperature of 28.0 oC, a pressure of 120 kPa, and a volume of 180 liters to a final state at a temperature of 320 oC, a pressure of 5.90 MPa, and a volume of 7.21 liters. The gas is first compressed and cooled at a constant pressure until its volume is 7.21 liters. Then the gas is then heated at constant volume until it final pressure is 5.90 MPa.
(A) Sketch the process on a P vs. V diagram and determine the work need to compress the gas along this path.
Ans:{20.7 kJ}

(B) Calculate the change in the internal energy of the gas between the initial and final state of the gas.
Ans:{27.1 kcal or 113 kJ}

(C) What is the net heat flow into (or out of) the gas between its initial and final states?
Ans:{22.1kcal or 92.7kJ}

Exam #3 W2000

1. A well insulated, massless cylinder is if partially filled with 150 grams of water at 38.0 oC. The cylinder is fitted with a piston of negligible mass that sets on top of the water initially. Heat is added until there is 2.60 moles of steam in the cylinder. The air pressure on the piston is 102 kPa and the molecular weight of a water molecule is 18. If no heat is lost to the environment:

2. Equal amounts of ice (at -4.50 oC) and water (at higher initial temperature To) are mixed together in an insulated container.

3. The compression ratio of a diesel engine is 15 to 1 (i.e., the final volume is 1/15 the initial volume. If air with a c V = 20.8 J/mole/K at 101 kPa and 20.0 oC is compressed quickly enough that no heat is lost:

4. When 2.40 kJ of work are done on an ideal gas, the volume of the gas is compressed from 129 liters to 78.0 liters. The initial temperature of the gas is 42.0 oC.