Chapter(s) :

Ch 3, 4 & 6

Due Date :
April 14, 2011
Total Problems / Points :
16 / 60


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Cengel & Boles: Ch 3:

3.26(2pts) -
Use either the NIST Webbook or the Thermal/Fluids Toolbox (TFT) Excel plug-in.
Use the default reference state for both the NIST and TFT.

3.29E(2pts) -
Use either the NIST Webbook or the Thermal/Fluids Toolbox (TFT) Excel plug-in.
Use the default reference state for both the NIST and TFT.

Cengel & Boles: Ch 4:
4.8(6pts) - Also calculate the total heat transfer, Q in kJ, for part (a) and again for part (b),
4.42(5pts) , 4.59E(4pts) , 4.60(4pts)

Special Problems
WB-1(5pts) , WB-2(8pts) , WB-3(6pts) , WB-4(3pts) , WB-5(3pts) , WB-6(3pts) , WB-7(3pts)

Cengel & Boles: Ch 6: 6.23(2pts), 6.41(2pts), 6.55(2pts)

WB-1 Clapeyron & Clausius-Clapeyron Equations - 5 pts
Statement :

Estimate the latent heat of vaporization, in Btu/lbm, of ammonia at -10oF using:

a.) The Clapeyron equation
b.) The Clausius-Clapeyron equation
c.) The ammonia tables (NIST)

  Hints :

The key to this problem is using the saturated NH3 tables (NIST) to obtain P*(T) data for use in the Clapeyron and Clausius-Clapeyron Equations.

Ans.: ΔHvap ≈ 600 Btu/lbm

WB-2 Hypothetical Process Paths and the Latent Heat of Vaporization - 8 pts
  Problem Statement : Use the hypothetical process path shown here to help you determine the change in enthalpy in Joules for 20.0 g of heptane (C7H16) as it changes from a saturated liquid at 300 K to a temperature of 370 K and a pressure of 58.7 kPa. Calculate the ΔH for each step in the path. Do not use tables of thermodynamic properties, except to check your answers. Instead, use the Antoine Equation to estimate the heat of vaporization of heptane at 300 K. Use the average heat capacity of heptane gas over the temperature range of interest. Assume heptane gas is an ideal gas at the relevant temperatures and pressures. Hypothetical Process Path
  Hints :

The key to the first step in this HPP is the Clausius-Clapeyron Equation. Use the Antoine equation to help you estimate the latent heat of vaporization at T1. In the second step, interpolate on the Cp data from the NIST WebBook to determine Cp(T1) and Cp(T2). Then, use the average of these two Cp's to evaluate the change in enthalpy. All you need to do is think a little bit and you will see how to evaluate ΔU34.

Ans.: ΔH12 ≈ 7000 J , ΔH23 ≈ 2500 J

WB-3 Work and Heat Transfer for a Closed, 3-Step Cycle - 6 pts
Statement :

A closed system undergoes a thermodynamic cycle consisting of the following processes:

  • Process 1-2: Adiabatic compression from P1 = 50 psia, V1 = 3.0 ft3 to V2 = 1 ft3 along a path described by : P V1.4 = constant, where V is the specific volume.
  • Process 2-3: Constant volume
  • Process 3-1: Constant pressure with U1 - U3 = 46.7 Btu.

There are no significant changes in kinetic or potential energies in any of these processes.

a.) Sketch this cycle on a PV Diagram.
b.) Calculate the net work for the cycle in Btu.
c.) Calculate the heat transfer for process 2-3.

  Hints :

The key to part (c) is to apply the 1st Law to the entire cycle and eliminate any terms that are negligible or zero.

Ans.: Wb ~ -20 Btu , Q23 ~ -85 Btu

WB-4 Heat Conduction Through a Composite Wall - 3 pts
Statement :

A composite plane wall consists of a 9 inch thick layer of brick and a 4 inch thick layer of insulation. The outer surface temperatures of the brick and insulation are 1260oR and 560oR, respectively, and there is perfect contact at the interface between the brick and the insulation. At steady-state, determine the heat conduction flux through the wall in Btu/h-ft2 and the temperature in oR at the interface between the brick and the insulation.

      Brick Insulation  
Data :   k 1.4 0.05 Btu/h-ft-oR
  Hints :

The key is to assume that the process operates at steady-state. In this case, all of the heat that arrives at the interface between the brick and the insulation by conduction through the brick must leave the interface as heat conduction through the insulation. Otherwise, the temperature at the interface would rise or fall as energy accumulated or was depleted at the interface.

Ans.: q ~ -100 Btu/h-ft2

WB-5 Combined Convection and Radiation Heat Loss - 3 pts
Statement :
A 3.0 m2 hot black surface at 80oC is losing heat to the surrounding air at 25oC by convection with a convection heat transfer coefficient of 12 W/m2-oC, and by radiation to the surrounding surfaces at 15oC. Determine the total rate of heat loss from the surface in W.
  Hints :

The key assumption here is that the emissivity of the surface is 1.0 because it is described as "black".

Ans.: Qtotal ~ 3500 W

WB-6 Minimum Insulation Thickness for a Hot Surface - 3 pts
Statement :
A flat surface is covered with insulation with a thermal conductivity of 0.08 W/m-K. The temperature at the interface between the surface and the insulation is 300oC. The outside of the insulation is exposed to air at 30oC and the convection heat transfer coefficient between the insulation and the air is 10 W/m2-K. Ignoring radiation heat transfer, determine the minimum thickness of the insulation, in m, such that the outside surface of the insulation is not hotter than 60oC at steady-state.
  Hints :

The key is that, at steady-state, energy cannot accumulate at the surface where the air touches the insulation.

Ans.: Lins ~ 0.06 m

WB-7 1st Law Analysis of Steam in a Closed System - 3 pts
Statement :

As shown in the figure below, 5.0 kg of steam contained within a piston-and-cylinder device undergoes an expansion from state 1 where the specific internal energy is 2709.9 kJ/kg to state 2 where the specific internal energy is 2659.6 kJ/kg. During the process, there is heat transfer to the steam with a magnitude of 80 kJ. Also, a paddle wheel transfers energy to the steam by work in the amount of 18.5 kJ. There is no significant change in the kinetic or gravitational potential energies of the steam. Determine the work done by the steam on the piston during the process in kJ. Note: the referenece state for steam is Usat liq = 0 kJ/kg at 0.01oC.

  Hints :

Making and applying the proper assumptions are the keys to solving this problem correctly.

Ans.: Wb ~ 350 kJ