Homework 3


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        Submitted Answers will be graded W 10/1, Th 10/2, F 10/3, and M 10/6 at 12:00 noon.

        Problem 3.1
          What you should learn: This is a quick practice problem in using the thermal expansion equation: ΔL = αLΔT

        Problem: An aluminum rod 1.00 m long is heated from a temperature of 0 °C to a final temperature Tf. How much does the length of the rod change? (You may refer to ΔL as DeltaL in the answer.)

        		  

        Constants and fixed variables:
          The coefficient of thermal expansion for aluminum, alpha: α = 26 x 10-6 °C-1
          Initial temperature, Ti: Ti = 0 °C
          Length of rod: L = 1.00 m

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        Answer Range: 2.00 - 3.20 mm
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        Problem 3.2
          What you should learn: The change in volume due to thermal expansion is: ΔV = βVΔT
        Problem: A mercury thermometer contains a volume of mercury V that expands from a bulb into a very narrow channel made by forming a glass rod around a wire that is later removed. The height of the mercury column in the channel increases by a distance h for a temperature rise of 1.00 °C. Find the diameter d (not radius) of the channel. You may ignore the thermal expansion of the glass in this calculation.  
        Constants and fixed variables:
         Volume of mercury: V = 0.120 cm3 (be sure to note the units!)
         Volume coefficient of thermal expansion (beta) for mercury: β = 1.82 x 10-4 °C-1
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        Answer Range: 0.0800 - 0.140 mm
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        Problem 3.3
          What you should learn: The ideal gas law is PV = nRT. Sometimes this law seems a little complicated as there are four different quantities that can vary in a problem. This is an exercise in using the equation in two different types of applications.
        Problem: One liter (= 0.001 m3) of He gas at an initial temperature Ti and atmospheric pressure undergoes two different process that reduce its volume to the same final value. The first process is cooling to liquid nitrogen temperature at constant pressure and the second is compressing at constant room temperature. What pressure is required to accomplish this?  
        Constants and fixed variables:
          Volume of the gas V = 1.00 x 10–3 m3
          Liquid nitrogen temperature: Tf = –196 °C
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        Answer Range: 3.70 x 105 - 4.70 x 105 Pa
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        Problem 3.4
          What you should learn: The ideal gas law can also be expressed in terms of density.

        Problem: Using the ideal gas law and M, the molar mass, (the mass of one mole in g / mole), find the density ρ of an ideal gas in units of kg/m3. (Call this density rho = ρ. Submit an algebraic answer for rho in terms of P, R, T, and M.)

        		  
        Hints:
          How can density relate to the ideal gas law?
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        Problem 3.5
          What you should learn: The ideal gas law can be written either as PV = nRT or PV = NkT. When we deal with numbers of molecules, the second form can be more useful. Remember that N can vary in a problem, although it is usually fixed.
        Problem: An oven that has a volume of V is heated from temperature Ti to Tf  at constant atmospheric pressure. How many molecules of air leave the oven? (Call this number DeltaN.)  
        Constants and fixed variables:
          Atmospheric pressure, P0:  P0 = 1.01 x 105 Pa
          Boltzmann's constant:  k =  1.38 x 10–23 J / K
          Ideal gas constant: R = 8.314 J / mol·K
          Initial temperature, Ti: Ti = 20 °C
          Final temperature, Tf: Tf = 180 °C
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        Answer Range: 2.90 x 1024 - 5.90 x 1024 molecules
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        Problem 3.6
          What you should learn: This is a typical calorimetry problem. The net change in heat in an isolated (well-insulated) system is zero. Q = mcΔT and Q = ±mL are needed in these problems.
        Problem: A piece of copper of mass mc is heated and dropped into water in a calorimeter. Find Tfinal, the final temperature of the water.  

        Constants and fixed variables:
          Initial temperature of the copper: T0c = 87.0 °C
          Initial temperature of the water: T0w = 20.0 °C
          Mass of water: mw = 300 g
          Specific heat of copper: cc = 387 J/kg·°C
          Specific heat of water: cw = 4186 J/kg·°C

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        Answer Range: 21 - 25 °C
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        Problem 3.7
          What you should learn: This is calorimetry problem with a phase change.
        Problem: A piece of copper of mass mc is cooled and dropped into water in a calorimeter. The water freezes and then reaches an equilibrium temperature Tf. Find T0c the original temperature of the copper.  

        Constants and fixed variables:
          Mass of the copper: mc = 1300 g 
          Mass of the water: mw = 200 g
          Initial temperature of the water: T0w = 20.0 °C
          Specific heat of copper: cc = 387 J/kg·°C
          Specific heat of water: cw = 4186 J/kg·°C
          Specific heat of ice: ci = 2090 J/kg·°C
          Latent heat of fusion for water: Lf = 3.33 x 105 J/kg
          Latent heat of vaporization for water: Lv = 2.26 x 106 J/kg

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        Answer Range: -210 to -180 °C
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        Problem 3.8
          What you should learn: dW = -pdV is the work done in changing the volume of a gas by a small amount. We integrate this to determine the work done in a process where the change of volume is not infinitesimal.
        Problem: A volume of gas is placed in a cylinder. The gas initially occupies a volume V1 and at a pressure P1 and temperature T0. The cylinder is paced in a water bath so its temperature remains fixed. The gas is then compressed to half the initial volume. What is the total work W done on the gas in this process?  

        Constants and fixed variables:
          Initial volume of the gas: V1 = 1.24 x 10-3 m3
          Initial pressure: P1 = 1.24 x 105 Pa
          Boltzmann's constant:  k =  1.38 x 10–23 J / K
          Ideal gas constant: R = 8.314 J / mol·K

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        Answer Range: 90 - 120 J
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        Problem 3.9
          What you should learn: This is an application of the First Law: ΔEint = Q + W.
        Problem: A volume V0 of ideal gas is initially at a temperature T0 and at atmospheric pressure P0. The gas is heated at constant pressure until its temperature is T1. By what amount has the internal energy changed in this process?  (You may refer to ΔEint as Eint.)  

        Constants and fixed variables:
          Volume of the air: V0 = 2.44 x 10-3 m3
          Initial temperature of the air: T0 = 20 °C
          Atmospheric pressure: P0 = 1.01 x 105 Pa
          Heat capacity of the gas: C = 29.1 J/K
          Boltzmann's constant:  k =  1.38 x 10–23 J / K
          Ideal gas constant: R = 8.314 J / mol·K

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        Answer Range: 5100 - 7900 J
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          • This is the end of HW 3 - More problems from Chapter 20 will be HW 4.


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