ATTEMPT ALL QUESTIONS. BE SURE TO ANSWER

A body with mass m = 1 2 kg is attached to the end of a spring that is stretched 2 m by a force of 100 N. Furthermore, there is also attached a dashpot4 that provides 6 N of resistance for each m/s of velocity. If the mass is set in motion by further stretching the spring 1 2 m and giving it an upward velocity of 10 m/s, let us find the subsequent motion.

5-180 Determine the power input for a compressor that compresses helium from 150 kPa and 20C to 400 kPa and 200C. Helium enters this compressor through a 0.1-m2 pipe at a velocity of 15 m/s. 5-181 Refrigerant 134a enters a compressor with a mass flow rate of 5 kg/s and a negligible velocity. The refrigerant enters the compressor as a saturated vapor at 10C and leaves the compressor at 1400 kPa with an enthalpy of 281.39 kJ/kg and a velocity of 50 m/s. The rate of work done on the refrigerant is measured to be 132.4 kW. If the elevation change between the compressor inlet and exit is negligible, determine the rate of heat transfer associated with this process, in kW

5-185 A tank with an internal volume of 1 m3 contains air at 800 kPa and 25 C. A valve on the tank is opened allowing air to escape and the pressure inside quickly drops to 150 kPa, at which point the valve is closed. Assume there is negligible heat transfer from the tank to the air left in the tank. (a) Using the approximation constant , calculate the mass withdrawn during the process. (ib) Consider the same process but broken into two parts. That is, consider an intermediate state at P2 = 400 kPa, calculate the mass removed during the process from Px = 800 kPa to P2 and then the mass removed during the process from P2 to P3 = 150 kPa, using the type of approximation used in part (a), and add the two to get the total mass removed. (c) Calculate the mass removed if the variation of he is accounted for

5-186 A liquid R-134a bottle has an internal volume of 0.001 m3. Initially it contains 0.4 kg of R-134a (saturated mixture) at 26C. A valve is opened and R-134a vapor only (no liquid) is allowed to escape slowly such that temperature remains constant until the mass of R-134a remaining is 0.1 kg. Find the heat transfer necessary with the surroundings to maintain the temperature and pressure of the R-134a constant. 5-187 f M-. Steam enters a turbine steadily at 7 MPa and 600C with a velocity of 60 m/s and leaves at 25 kPa with a quality of 95 percent. A heat loss of 20 kJ/kg occurs during the process. The inlet area of the turbine is 150 cm2, and the exit area is 1400 cm2. Determine (a) the mass flow rate of the steam, (b) the exit velocity, and (c) the power output

Reconsider Prob. 5-187. Using EES (or other) N Ss software, investigate the effects of turbine exit area and turbine exit pressure on the exit velocity and power output of the turbine. Let the exit pressure vary from 10 to 50 kPa (with the same quality), and the exit area to vary from 1000 to 3000 cm2. Plot the exit velocity and the power outlet against the exit pressure for the exit areas of 1000, 2000, and 3000 cm2, and discuss the results. 5-189 In large gas-turbine power plants, air is preheated by the exhaust gases in a heat exchanger called the regenerator before it enters the combustion chamber. Air enters the regenerator at 1 MPa and 550 K at a mass flow rate of 800 kg/min. Heat is transferred to the air at a rate of 3200 kJ/s. Exhaust gases enter the regenerator at 140 kPa and 800 K and leave at 130 kPa and 600 K. Treating the exhaust gases as air, determine (a) the exit temperature of the air and (b) the mass flow rate of exhaust gases

5-190 It is proposed to have a water heater that consists of an insulated pipe of 5-cm diameter and an electric resistor inside. Cold water at 20C enters the heating section steadily at a rate of 30 L/min. If water is to be heated to 55C, determine (a) the power rating of the resistance heater and (b) the average velocity of the water in the pipe. 5-191 An insulated vertical piston-cylinder device initially contains 0.11 m1 of air at 150 kPa and 22C. At this state, a linear spring touches the piston but exerts no force on it. The cylinder is connected by a valve to a line that supplies air at 700 kPa and 22C. The valve is opened, and air from the high-pressure line is allowed to enter the cylinder. The valve is turned off when the pressure inside the cylinder reaches 600 kPa. If the enclosed volume inside the cylinder doubles during this process, determine (a) the mass of air that entered the cylinder, and (b) the final temperature of the air inside the cylinder.

5-192 A piston-cylinder device initially contains 2 kg of refrigerant-134a at 800 kPa and 80C. At this state, the piston is touching on a pair of stops at the top. The mass of the piston is such that a 500-kPa pressure is required to move it. A valve at the bottom of the tank is opened, and R-134a is withdrawn from the cylinder. After a while, the piston is observed to move and the valve is closed when half of the refrigerant is withdrawn from the tank and the temperature in the tank drops to 20C. Determine (a) the work done and (b) the heat transfer

5-193 The pump of a water distribution system is powered by a 6-kW electric motor whose efficiency is 95 percent. The water flow rate through the pump is 18 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa (absolute), respectively, determine (a) the mechanical efficiency of the pump and (b) the temperature rise of water as it flows through the pump due to the mechanical inefficiency

5-194 The hot-water needs of a household are met by a 60-L electric water heater whose heaters are rated at 1.6 kW. The hot-water tank is initially full with hot water at 80C. Somebody takes a shower by mixing a constant flow of hot water from the tank with cold water at 20C at a rate of 0.06 kg/s. After a shower period of 8 min, the water temperature in the tank is measured to drop to 60C. The heater remained on during the shower and hot water withdrawn from the tank is replaced by cold water at the same flow rate. Determine the mass flow rate of hot water withdrawn from the tank during the shower and the average temperature of mixed water used for the shower.

of ambient air required to avoid knock. 5-196 A pressure cooker is a pot that cooks food much faster than ordinary pots by maintaining a higher pressure and temperature during cooking. The pressure inside the pot is controlled by a pressure regulator (the petcock) that keeps the pressure at a constant level by periodically allowing some steam to escape, thus preventing any excess pressure buildup. Pressure cookers, in general, maintain a gage pressure of 2 atm (or 3 atm absolute) inside. Therefore, pressure cookers cook at a temperature of about 133C instead of 100C, cutting the cooking time by as much as 70 percent while minimizing the loss of nutrients. The newer pressure cookers use a spring valve with several pressure settings rather than a weight on the cover. A certain pressure cooker has a volume of 6 L and an operating pressure of 75 kPa gage. Initially, it contains 1 kg of water. Heat is supplied to the pressure cooker at a rate of 500 W for 30 min after the operating pressure is reached. Assuming an atmospheric pressure of 100 kPa, determine (a) the temperature at which cooking takes place and (b) the amount of water left in the pressure cooker at the end of the process.

5-197 A D0 = 10-m-diameter tank is initially filled with water 2 m above the center of a D = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through a L = 100-m-long pipe connected to the valve. The friction factor of the pipe is given to be / = 0.015, and the discharge velocity is expressed as 2gz where z is the water height above the V 1.5 +fL/D 5 center of the valve. Determine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve. 5-198 The velocity of a liquid flowing in a circular pipe of radius R varies from zero at the wall to a maximum at the pipe center. The velocity distribution in the pipe can be represented as V(r), where r is the radial distance from the pipe center. Based on the definition of mass flow rate m, obtain a relation for the average velocity in terms of V(r), R, and r.

5-200 A rigid container filled with an ideal gas is heated while the gas is released so that the temperature of the gas remaining in the container stays constant. This container has a single outlet. Derive an expression for the mass flow rate at the outlet as a function of the rate of pressure change in the container. 5-201 Consider an evacuated rigid bottle of volume V that is surrounded by the atmosphere at pressure P0 and temperature T0. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle during this filling process in terms of the properties of the system and the surrounding atmosphere

5-219 Pneumatic nail drivers used in construction require 0.02 ft3 of air at 100 psia and 1 Btu of energy to drive a single nail. You have been assigned the task of designing a compressed-air storage tank with enough capacity to drive 500 nails. The pressure in this tank cannot exceed 500 psia, and the temperature cannot exceed that normally found at a construction site. What is the maximum pressure to be used in the tank and what is the tank's volume? 5-220 You have been given the responsibility of picking a steam turbine for an electrical-generation station that is to produce 300 MW of electrical power that will sell for $0.05 per kilowatt-hour. The boiler will produce steam at 700 psia and 700F, and the condenser is planned to operate at 80F. The cost of generating and condensing the steam is $0.01 per kilowatt-hour of electricity produced. You have narrowed your selection to the three turbines in the table below. Your criterion for selection is to pay for the equipment as quickly as possible. Which turbine should you choose?

5-221E You are to design a small, directional control rocket to operate in space by providing as many as 100 bursts of 5 seconds each with a mass flow rate of 0.5 lbm/s at a velocity of 400 ft/s. Storage tanks that will contain up to 3000 psia are available, and the tanks will be located in an environment whose temperature is 40F. Your design criterion is to minimize the volume of the storage tank. Should you use a compressed-air or an R-134a system?

5-222 An air cannon uses compressed air to propel a projectile from rest to a final velocity. Consider an air cannon 276 MASS AND ENERGY ANALYSIS that is to accelerate a 10-gram projectile to a speed of 300 m/s using compressed air, whose temperature cannot exceed 20C. The volume of the storage tank is not to exceed 0.1 m \ Select the storage volume size and maximum storage pressure that requires the minimum amount of energy to fill the tank.

5-223 To maintain altitude, the temperature of the air inside a hot-air balloon must remain within a 1C band, while the volume cannot vary by more than 1 percent. At a 300-m altitude, the air in a 1000 m3 hot-air balloon needs to maintain a 35C average temperature. This balloon loses heat at a rate of 3 kW through the fabric. When the burner is activated, it adds 30 kg/s of air at 200C and 100 kPa to the balloon. When the flap that allows air to escape is opened, air leaves the balloon at a rate of 20 kg/s. Design the burner and exhaust-flap control cycles (on time and off time) necessary to maintain the balloon at a 300-m altitude. that is to accelerate a 10-gram projectile to a speed of 300 m/s using compressed air, whose temperature cannot exceed 20C. The volume of the storage tank is not to exceed 0.1 m3 . Select the storage volume size and maximum storage

1.4. Prove (a) Theorem 1-1, (b) Theorem 1-2, (c) Theorem 1-3, page 5. (a) We have A, = A, U (A, - A, ) where A, and A, - A, are mutually exclusive. Then by Axiom 3, page 5: P(A,) = P(A,) + P(A, - A,) so that P(A, - A ) = P(A,) - P(A,) Since P(A, - A,) 2 0 by Axiom 1, page 5, it also follows that P(A, ) = P(A, ). (b) We already know that P(A) 2 0 by Axiom 1. To prove that P(A)