Ch 12 Homework Name: Homework problems are from the Serway & Vuille 10 th edition. Follow the instructions and show your work clearly. 1. (Problem 1) An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8000 g and an area of 5.00 cm 2 and is free to slide up and down, keeping the pressure of the gas constant. (a) Draw a diagram of the cylinder and label all the physical quantities using variables you choose. (b) How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from 20.0 C to 300 C? (c) What kind of thermal process is the part (b)?
(d) What does the sign of your answer to part (b) indicate? 2. (Problem 5) A gas expands from I to F along the three paths indicated in the figure below. Calculate the work done on the gas along paths (a) IAF, (b) IF, and (c) IBF. (a) Calculate the work done on the gas along paths IAF.
(b) Calculate the work done on the gas along paths IAF. (c) Calculate the work done on the gas along paths IAF.
3. (Problem12) A cylinder of volume 0.300 m 3 contains 10.0 mol of neon gas at 20.0 C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? (b) Find the internal energy of the gas. (c) Suppose the gas expands at constant pressure to a volume of 1.000 m 3. How much work is done on the gas? (d) What is the temperature of the gas at the new volume? (e) Find the internal energy of the gas when its volume is 1.000m 3.
(f) Compute the change in the internal energy during the expansion. (g) Compute. (h) Must thermal energy be transferred to the gas during the constant pressure expansion or be taken away? (i) Compute Q, the thermal energy transfer. (j) What symbolic relationship between Q, U, and W is suggested by the values obtained?
4. (Problem 19) An ideal gas is compressed from a volume of V i =4.00 L to a volume of V f = 3.00 L while in thermal contact with a heat reservoir at T = 295 K as in the figure above. During the compression process, the piston moves down a distance of d = 0.130 m under the action of an average external force of F = 25.0 kn. (a) Find the work done on the gas. (b) Find the change in internal energy of the gas. (c) Find the thermal energy exchanged between the gas and the reservoir.
(d) If the gas is thermally insulated so no thermal energy could be exchanged, what would happen to the temperature of the gas during the compression? 5. (Problem 29) A gas increases in pressure from 2.00 atm to 6.00 atm at a constant volume of 1.00 m 3 and then expands at constant pressure to a volume of 3.00 m 3 before returning to its initial state as shown in the figure below. How much work is done in one cycle? (a) How much work is done by the gas as the gas increases in pressure from 2.00 atm to 6.00 atm at a constant volume of 1.00 m 3?
(b) How much work is done by the gas as the gas expands at constant pressure 6.00 atm to a volume of 3.00 m 3? (c) How much work is done by the gas as the gas return to its initial state as shown in the figure above? (d) How much work is done in one cycle? (e) Work done in one cycle equals the area enclosed by the triangle in the figure above. Calculate the areas of the triangle and compare the result with the answer in the part (d).
6. (Problem 32) A heat engine is being designed to have a Carnot efficiency of 65% when operating between two heat reservoirs. (a) If the temperature of the cold reservoir is 20 C, what must be the temperature of the hot reservoir? (b) Can the actual efficiency of the engine be equals to 65%? Explain your answer. 7. (Problem 45) A Styrofoam cup holding 125 g of hot water at C cools to room temperature, 20.0 C. What is the change in entropy of the room? (Neglect the specific heat of the cup and any change in temperature of the room)
8. (Problem 56) A weightlifter has a basal metabolic rate of 80.0 W. As he is working out, his metabolic rate increases by about 650 W. (a) How many hours does it take him to work off a 450-Calorie bagel if he stays in bed all day? (1 Calorie = 4186 J) (Hint: Power = Energy used/ time) (b) How long does it take him if he s working out? (c) Calculate the amount of mechanical work necessary to lift a 120-kg barbell 2.00 m. (Hint: work = Force distance)
(d) He drops the barbell to the floor and lifts it repeatedly. How many times per minute must he repeat this process to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise? (e) Could he actually do repetition at the rate found in part (d) at the given metabolic level? Explain.