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Homework Help: Specific Heat Capacity and Change in Internal Energy

  1. May 23, 2007 #1
    1. The problem statement, all variables and given/known data
    I'm having trouble with the following two problems:

    1. A jar of tea is placed in the sunlight until it reaches an equilibrium temperature of 32*C. In an attempt to cool the liquid, which has a mass of .180kg, .112 kg of ice at 0*C is added. At the time at which the temperature of the tea (and melted ice) is 15*C, determine the mass of the remaining ice in the jar. Assume the Specific heat capacity of the tea to be that of pure liquid water.

    2. The heaviest snake ever found had a mass of 227 kg and measured 8.45 m in length. Suppose a sample of a gas with an initial internal energy of 42.0 kJ performs an amount of work equal to that needed to lift the snake to a height equal to its length. If 4.00 kJ of energy is transferred to the gas by heat during the lifting process, what will be the final internal energy of the gas?

    2. Relevant equations

    1. C[p,t] * M [t] * (T[f]-T) = C[p,i] * M * (T[f]-T)
    Specific Heat of Water = 4.186 x 10 ^ 3.
    Specific Heat of Ice = 2.09 x 10 ^ 3

    2. PE + KE + U = 0
    PE = m*g*h
    KE = .5m * V ^ 2
    3. The attempt at a solution

    1. (4.186 * 10 ^3) (.180kg) (17) = (2.09 x 10 ^ 3)(.112kg)(15)
    I am unaware of how to account for the melted and remaining ice.
    Do i just do like a mass initial and final?

    2. (227 kg) * (8.45 m) * (9.81) = 18, 817 J I really don't think im anywhere close to the right answer.

    Your help is greatly appreciated.
  2. jcsd
  3. May 23, 2007 #2

    Doc Al

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    Staff: Mentor

    When the tea cools from its initial temperature to 15C, how much energy is released? How much ice can be melted and then warmed to 15C by that amount of energy?

    The gas (a) does some work and (b) has heat flow into it. What's the net change in internal energy? What's the final internal energy?
  4. May 23, 2007 #3
    Would i be using the latent heat equation to figure this out? Q = mL? And if so would i use the latent heat of water? or would i use the specific heat cpacity equation? C[p] = energy transfered as heat/ (mass* change in temperature)
  5. May 23, 2007 #4

    Doc Al

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    Staff: Mentor

    You'll need to use both. The ice first needs to be melted (latent heat of fusion) and then the resulting water needs to be heated (specific heat of water).

    You'll to set up an equation and solve for the unknown mass of ice that melts.
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