Homework 4


        Never enter units in your answers. Be sure to use the units indicated on the HW submission page.
        Enter numbers without commas. 23,546 should be 23546
        Always enter a * for multiplication. g(H+h) should be g*(H+h).


        Return to Physics 123 Home page.
         

        Enter your CID:             

        Enter your password:    

        You are now obtaining input data for CID =
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.

        Submitted Answers will be graded W 10/8, Th 10/9, F 10/10, and M 10/13 at 12:00 noon.


        Problem 4.1
          What you should learn: The first 12 (short)  problems are applications of the First Law of Thermodynamics to the "basic processes." ΔEint = Q + W.  You will need to apply the ideal gas law, remember that Eint is proportional to T, and that Q = 0 for adiabatic processes, among other things.

        Problem: A certain amount of ideal gas is placed in a cylinder and a piston is put on top of the gas. The gas can undergo processes at constant volume, temperature, and pressure, and can also undergo adiabatic processes. In the next problems, you are to find Q, W, and Eint for each process. The first process is a constant temperature process. The volume is reduced to half the initial volume. What is Q for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: –130 to –100 J
        Submit HW answers.


        Problem 4.2
          What you should learn:  ΔEint = Q + W. 

        Problem:  The volume is reduced to half the initial volume in a constant temperature process. What is W for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 100 - 130 J
        Submit HW answers.


        Problem 4.3
          What you should learn:  ΔEint = Q + W. 

        Problem:  The volume is reduced to half the initial volume in a constant temperature process. What is ΔEint for the process? (You may call this Eint.)

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: -20 J to +20 J
        Submit HW answers.


        Problem 4.4
          What you should learn:  ΔEint = Q + W. 

        Problem:  The pressure is doubled in a constant volume process. What is W for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: -20 J to +20 J
        Submit HW answers.


        Problem 4.5
          What you should learn:  ΔEint = Q + W. 

        Problem:  The pressure is doubled in a constant volume process. What is Q for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 220 - 280 J
        Submit HW answers.


        Problem 4.6
          What you should learn:  ΔEint = Q + W. 

        Problem:  The pressure is doubled in a constant volume process. What is ΔEint for the process? (You may call this Eint.)

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range:  210 - 290 J
        Submit HW answers.


        Problem 4.7
          What you should learn:  ΔEint = Q + W. 

        Problem:  The temperature increases 100 °C in a constant pressure process. What is W for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: –65 to –50 J
        Submit HW answers.


        Problem 4.8
          What you should learn:  ΔEint = Q + W. 

        Problem:  The temperature increases 100 °C in a constant pressure process. What is Q for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 125 - 160 J
        Submit HW answers.


        Problem 4.9
          What you should learn:  ΔEint = Q + W. 

        Problem:  The temperature increases 100 °C in a constant pressure process. What is ΔEint for the process? (You may call this Eint.)

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 75 - 100 J
        Submit HW answers.


        Problem 4.10
          What you should learn:  ΔEint = Q + W. 

        Problem:  The volume is reduced to half the initial volume in an adiabatic process. What is W for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 130 - 170 J
        Submit HW answers.


        Problem 4.11
          What you should learn:  ΔEint = Q + W. 

        Problem:  The volume is reduced to half the initial volume in an adiabatic process. What is Q for the process?

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints: –10 to 10 J
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range:
        Submit HW answers.


        Problem 4.12
          What you should learn:  ΔEint = Q + W. 

        Problem:  The volume is reduced to half the initial volume in an adiabatic process. What is ΔEint for the process? (You may call this Eint.)

        		  

        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, T1: T1= 20 °C
          Initial volume, V1: V1 = 1.24 x 10-3 m3
          Molar specific heat at constant volume, Cv: CV = 3R/2

        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints: 130 - 170 J
        Some useful relationships.
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range:
        Submit HW answers.



        Problem 4.13
          What you should learn: The thermal conductivity equation gives the energy per unit time passing through a material with a thermal gradient across it. The equation is P =  k A | ΔT / Δx |
        Problem: In one hour, how much energy passes through a pane of glass of area A and thickness d when the outside temperature is To and the inside temperature is Ti? (You may call the energy E.)  
        Constants and fixed variables:
          Outside temperature To = –20 °C
          Inside temperature Ti = +20 °C
          Area of the glass pane A = 1.24 m2
          Thermal conductivity of glass k = 0.800 W/m·°C 
        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        How does power relate to energy?
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 23,000,000 - 48,000,000 J
        Submit HW answers.



        Problem 4.14
          What you should learn: When more than one layer is present, you can make use of the fact that in steady state, the heat flow through each layer is equal.
        Problem: To reduce energy loss in the window of Problem 4.13, you decide to make a double-paned window with two thicknesses of glass and a layer of air in between. How much energy now passes through the glass in one hour? (Call this E.)  
        Constants and fixed variables:
          Thermal conductivity of air kair = 0.0234 W/m·°C 
          Thickness of air layer dair = 2.00 mm.
        Variables that must be changed with each submission:
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Hints:
        I don't know the temperature across each individual layer. What do I do?
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Answer Range: 1,800,000 - 2,000,000 J
        Submit HW answers.



        Problem 4.15
          What you should learn: This is primarily an exercise in counting degrees of freedom. Recall that CV = R/2 times the number of degrees of freedom.
        Problem: There are n moles of hydrogen gas initially at room temperature. The gas is heated at constant pressure. If the heat introduced into the gas is Q, by how much does the temperature rise? Give your answer as an algebraic expression in terms of Q, R, and n. Treat the hydrogen as an ideal diatomic gas. You may call the rise in temperature DeltaT.  
        Constants and fixed variables:
          The ideal gas constant: R = 8.314 J / mol·K
        Hints:
        There seems to be a step I'm missing...
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Submit HW answers.



        Problem 4.16
          What you should learn: This is an exercise in counting degrees of freedom associated with translation, rotation, and vibration
        Problem: For the volume of gas described in Problem 14, find an algebraic expression for the average rotational energy of a hydrogen molecule at room temperature. Express your answer in terms of Boltzmann's constant kB  and temperatire T. You may call this average energy Eave.  
        Results of previous submissions:
        Submission Score Your Answer Correct Answer Comments
        Database Results Wizard Error
        The operation failed. If this continues, please contact your server administrator.
        Submit HW answers.



        Return to Physics 123 Home page.