ENGG 360: Thermodynamics Home Assignment 1 (Chapter 1) (Answer) 1. Why does a bicyclist pick up speed on a downhill road even when he is not pedaling? Does this violate the conservation of energy principle? a. On a downhill road the potential energy of the bicyclist is being converted to kinetic energy, and thus the bicyclist picks up speed. b. There is no creation of energy, and thus no violation of the conservation of energy principle.. An office worker claims that a cup of cold coffee on his table warmed up to 80 by picking up energy from the surrounding air, which is at 5. Is there any truth to his claim? Does this process violate any thermodynamic laws? a. There is no truth to his claim. b. It violates the second law of thermodynamics. 3. Determine the mass and the weight of the air contained in a room whose dimensions are 6 m 6 m 8 m. Assume the density of the air is 1.16 kg/m 3. a. Assumptions: The density of air is constant throughout the room. b. Properties: The density of air is given to be ρ = 1.16 kg/m 3. The mass of the air in the room is 3 m = ρv = (1.16 kg/m )(6 6 8 m ) = 334.1kg W = mg = (334.1 kg)(9.81 m/s 3 1 N ) 1 kg m/s = 377 N ROOM AIR 4. A 3-kg rock is thrown upward with a force of 00 N at a location where the local gravitational acceleration is 9.79 m/s. Determine the acceleration of the rock, in m/s. a. The weight of the rock is: 1 N W = mg = (3 kg)(9.79 m/s ) = 9.37 N 1 kg m/s b. Then the net force that acts on the rock is: F net = Fup Fdown = 00 9.37 = 170.6 N Stone
From the Newton's second law, the acceleration of the rock becomes a = F m 170.6 N 1 kg m/s = 3 kg 1 N = 56.9 m/s 5. While solving a problem, a person ends up with the equation E = 5 kj + 7 kj/kg at some stage. Here E is the total energy and has the unit of kilojoules. Determine how to correct the error and discuss what may have caused it. The two terms on the right-hand side of the equation E = 5 kj + 7 kj/kg do not have the same units; therefore, they cannot be added to obtain the total energy. Multiplying the last term by mass will eliminate the kilograms in the denominator; moreover, the whole equation will become dimensionally homogeneous. Every term in the equation will have the same unit. Discussion Obviously this error was caused by forgetting to multiply the last term by mass at an earlier stage. 6. A 4-kW resistance heater in a water heater runs for hours to raise the water temperature to the desired level. Determine the amount of electric energy used in both kwh and kj. The resistance heater consumes electric energy at a rate of 4 kw or 4 kj/s. Then the total amount of electric energy used in hours becomes a. Total energy = (Energy per unit time)(time interval) = (4 kw)( h) = 8 kwh b. Noting that 1 kwh = (1 kj/s)(3600 s) = 3600 kj, Total energy = (8 kwh)(3600 kj/kwh) = 8,800 kj Discussion Note kw is a unit for power whereas kwh is a unit for energy. 7. You have been asked to do a metabolism (energy) analysis of a person. How would you define the system for this purpose? What type of system is this?
a. This system is a region of space or open system in that mass such as air and food can cross its control boundary. The system can also interact with the surroundings by exchanging heat and work across its control boundary. b. By tracking these interactions, we can determine the energy conversion characteristics of this system. 8. You are trying to understand how a reciprocating air compressor (a piston-cylinder device) works. What system would you use? What type of system is this? a. The system is taken as the air contained in the piston-cylinder device. b. This system is a closed or fixed mass system since no mass enters or leaves it. 9. What is the difference between intensive and extensive properties? Intensive properties do not depend on the size (extent) of the system. However, extensive properties do. 10. Is the weight of a system an extensive or intensive property? If we were to divide the system into smaller portions, the weight of each portion would also be smaller. Therefore, the weight is an extensive property. 11. For a system to be in thermodynamic equilibrium, do the temperature and the pressure have to be the same everywhere? For a system to be in thermodynamic equilibrium, the temperature has to be the same throughout but the pressure does not. However, there should be no unbalanced pressure forces present. The increasing pressure with depth in a fluid, for example, should be balanced by increasing weight. 1. What is the state postulate? The state of a simple compressible system is completely specified by two independent, intensive properties. 13. How would you describe the state of the water in a bathtub? How would you describe the process that this water experiences as it cools?
a. The pressure and temperature of the water are normally used to describe the state. Chemical composition, surface tension coefficient, and other properties may be required in some cases. b. As the water cools, its pressure remains fixed. This cooling process is then an isobaric process. 14. When analyzing the acceleration of gases as they flow through a nozzle, what would you choose as your system? What type of system is this? a. When analyzing the acceleration of gases as they flow through a nozzle, the proper choice for the system is the volume within the nozzle, bounded by the entire inner surface of the nozzle and the inlet and outlet cross-sections. b. This is a control volume since mass crosses the boundary. 15. When is a steady-flow process? If a process involves no changes with time anywhere within the system or at the system boundaries, the process is said to be steady-flow. 16. What is the zeroth law of thermodynamics? The zeroth law of thermodynamics states that: Two bodies are in thermal equilibrium if both have the same temperature reading, even if they are not in contact. 17. The deep body temperature of a healthy person is 37.What is it in kelvins? The Kelvin scale is related to Celsius scale by T(K) = T( C) + 73 Therefore, T(K) = 37 C + 73 = 310 K 18. What is the difference between gage pressure and absolute pressure? a. The pressure relative to the atmospheric pressure is called the gage pressure. b. The pressure relative to an absolute vacuum is called absolute pressure. 19. Someone claims that the absolute pressure in a liquid of constant density doubles when the depth is doubled. Do you agree? Explain.
No, the absolute pressure in a liquid of constant density does not double when the depth is doubled. It is the gage pressure that doubles when the depth is doubled. 0. A tiny steel cube is suspended in water by a string. If the lengths of the sides of the cube are very small, how would you compare the magnitudes of the pressures on the top, bottom, and side surfaces of the cube? If the lengths of the sides of the tiny cube suspended in water by a string are very small The magnitudes of the pressures on all sides of the cube will be the same. 1. The pressure in a compressed air storage tank is 1500 kpa. What is the tank s pressure in 1 kn and m units; kg, m, and s units; and 3 kg, km, and s units? Using appropriate conversion factors, we can obtain 1 P = (1500 kpa) = 1500 kn/m 1000 kg m/s P = (1500 kpa) = 1,500,000 kg/m s 3 1000 kg m/s 1000 m P = (1500 kpa) = 1,500,000, 000 kg/km s 1kN 1kN 1km