ENGR 2345THERMODYNAMICSFINAL EXAMDUE: 9DEC 2014
Work two (2) problems from each chapter using the following list:
2.111, 2.118, and 2-125
3-114, 3-117, and 3-127
4-125, 4-139, and 4-148
5-150, 5-170, and 5-177
2.11) A hollow spherical iron container is filled with iced water at 0°C. The rate of heat loss from the sphere and the rate at which ice melts in the container are to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified values. 2 Heat transfer through the shell is one-dimensional. 3 Thermal properties of the iron shell are constant. 4 The inner surface of the shell is at the same temperature as the iced water, 0°C.
Properties The thermal conductivity of iron is k = 80.2 W/mC (Table 2-3). The heat of fusion of water is at 1 atm is 333.7 kJ/kg.
Find the surface area: A = D2 then and find
2-118 The heating and cooling costs of a poorly insulated house can be reduced by up to 30 percent by adding adequate insulation. The time it will take for the added insulation to pay for itself from the energy it saves is to be determined.
Assumptions It is given that the annual energy usage of a house is $1200 a year, and 46% of it is used for heating and cooling. The cost of added insulation is given to be $200.
AnalysisThe amount of money that would be saved per year is determined directly from Money saved and then find the simple Payback Period.
2-125E The power required to pump a specified rate of water to a specified elevation is to be determined.
Properties The density of water is taken to be 62.4 lbm/ft3 (Table A-3E).
Analysis The required power is determined from
3-114 Carbon dioxide flows through a pipe at a given state. The volume and mass flow rates and the density of CO2 at the given state and the volume flow rate at the exit of the pipe are to be determined.
Analysis
(a)The volume and mass flow rates may be determined from ideal gas relation as
then find and then the density
(b) The volume flow rate at the exit is
3-117 A rigid container that is filled with R-13a is heated. The initial pressure and the final temperature are to be determined.
AnalysisThe initial specific volume is 0.090 m3/kg. Using this with the initial temperature reveals that the initial state is a mixture. The initial pressure is then the saturation pressure,
This is a constant volume cooling process (v= V /m = constant). The final state is superheated vapor and the final temperature is then
3-127 The pressure in an automobile tire increases during a trip while its volume remains constant. The percent increase in the absolute temperature of the air in the tire is to be determined.
Assumptions 1 The volume of the tire remains constant. 2 Air is an ideal gas.
PropertiesThe local atmospheric pressure is 90 kPa.
AnalysisThe absolute pressures in the tire before and after
P1 = Pgage,1+ Patm, P2 = Pgage,2+ Patm,
4-125 A cylinder equipped with an external spring is initially filled with air at a specified state. Heat is transferred to the air, and both the temperature and pressure rise. The total boundary work done by the air, and the amount of work done against the spring are to be determined, and the process is to be shown on a P-vdiagram.
Assumptions1 The process is quasi-equilibrium. 2 The spring is a linear spring.
Analysis
(a) The pressure of the gas changes linearly with volume during this process, and thus the process curve on a P-V diagram will be a straight line. Then the boundary work during this process is simply the area under the process curve, which is a trapezoidal. Thus,
(b)If there were no spring, we would have a constant pressure
process at P = 100 kPa. The work done during this process is
,
4-139 A man drinks one liter of cold water at 3°C in an effort to cool down. The drop in the average body temperature of the person under the influence of this cold water is to be determined.
Assumptions 1 Thermal properties of the body and water are constant. 2 The effect of metabolic heat generation and the heat loss from the body during that time period are negligible.
Properties The density of water is very nearly 1 kg/L, and the specific heat of water at room temperature is c = 4.18 kJ/kg·°C (Table A-3). The average specific heat of human body is given to be 3.6 kJ/kg.°C.
Analysis. The mass of the water is
We take the man and the water as our system, and disregard any heat and mass transfer and chemical reactions. Of course these assumptions may be acceptable only for very short time periods, such as the time it takes to drink the water. Then the energy balance can be written as
or
4-148 A piston-cylinder device contains an ideal gas. An external shaft connected to the piston exerts a force. For an isothermal process of the ideal gas, the amount of heat transfer, the final pressure, and the distance that the piston is displaced are to be determined.
Assumptions1 The kinetic and potential energy changes are negligible, . 2 The friction between the piston and the cylinder is negligible.
Analysis(a) We take the ideal gas in the cylinder to be the system. This is a closed system since no mass crosses the system boundary. The energy balance for this stationary closed system can be expressed as
(b) The relation for the isothermal work of an ideal gas may be used to determine the final volume in the cylinder. But we first calculate initial volume
, ,
(c) The final position of the piston and the distance that the piston is displaced are
, find
5-150Steam expands in a turbine whose power production is 9000 kW. The rate of heat lost from the turbine is to be determined.
Assumptions1 This is a steady-flow process since there is no change with time. 2 Kinetic and potential energy changes are negligible.
Properties From the steam tables (Tables A-6 and A-4)
AnalysisWe take the turbine as the system, which is a control volume since mass crosses the boundary. Noting that there is one inlet and one exiti the energy balance for this steady-flow system can be expressed in the rate form as
Find
5-170E Steam is mixed with water steadily in an adiabatic device. The temperature of the water leaving this device is to be determined.
Assumptions1 This is a steady-flow process since there is no change with time. 2 Kinetic and potential energy changes are negligible. 3 There are no work and heat interactions. 4 There is no heat transfer between the mixing device and the surroundings.
Analysis We take the mixing device as the system, which is a control volume. The energy balance for this steady-flow system can be expressed in the rate form as
From a mass balance
Theenthalpies of steam and water are (Table A-6E and A-4E)
Substituting into the energy balance equation solving for the exit enthalpy gives h3
At the exit state P3=60 psia and h3=65.19 kJ/kg. An investigation of Table A-5E reveals that this is compressed liquid state. Approximating this state as saturated liquid at the specified temperature, the temperature may be determined from Table A-4E to be
5-177 A fan is powered by a 0.5 hp motor, and delivers air at a rate of 85 m3/min. The highest possible air velocity at the fan exit is to be determined.
Assumptions 1This is a steady-flow process since there is no change with time at any point and thus . 2 The inlet velocity and the change in potential energy are negligible, . 3 There are no heat and work interactions other than the electrical power consumed by the fan motor. 4 The efficiencies of the motor and the fan are 100% since best possible operation is assumed. 5 Air is an ideal gas with constant specific heats at room temperature.
Properties The density of air is given to be = 1.18 kg/m3. The constant pressure specific heat of air at room temperature is cp= 1.005 kJ/kg.C (Table A-2).
Analysis We take the fan-motor assembly as the system. This is a control volume since mass crosses the system boundary during the process. We note that there is only one inlet and one exit, and thus The velocity of air leaving the fan will be highest when all of the entire electrical energy drawn by the motor is converted to kinetic energy, and the friction between the air layers is zero. In this best possible case, no energy will be converted to thermal energy, and thus the temperature change of air will be zero, Then the energy balance for this steady-flow system can be expressed in the rate form as
Noting that the temperature and thus enthalpy remains constant, the relation above simplifies further to
wheresolve for V2