PHY 126-07 Mid-term Exam II

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PHY 126-07 Mid-term Exam II
Chapters 15,16,17,18
You need to write how you have derived the
answers. Just writing an answer does not get you
the full point. When you use symbols that
you define, make clear what these symbols
represent.

• Problem 1 (1010 points)

A scientist is making a mockup model of a human
ear using a small can with the top surface open
and the bottom closed. A human ear is especially
sensitive to sound whose frequency is 3,440 Hz.
If this is the lowest frequency that the ear is
especially sensitive to, (a) what the height of
the mockup model h should be? Assume that the
speed of sound is 344 m/s. (b) What is the next
lowest frequency the ear especially sensitive to?
open
h
closed
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• Problem 2 (333335 points)

• 6.00 kg of ice at -5.00oC is added to a cooler
  holding 30 liters of water at 20.0oC. The
• density of water is 1000 kg/m3. The latent heat
  of fusion of water LL is 3.33 x 105 J/kg,
• the specific heat of water cwater and ice cice
  are 4190 and 2090 J/(kg K), respectively.
• What is the mass of 30-liter water mwater ?
• To melt 6.00 kg of ice how much heat Qmelt is
  needed?
• To change the temperature of the ice to 0.00oC
  how much of heat Qice is needed?
• Once all the ice melts how much of heat
  Qice-water is needed to raise the temperature of
• the water from the ice to T?
• To lower the temperature of 30 liter water from
  20.0oC to T, how much heat Qwater is
• needed?
• (f) What temperature of the water T when it comes
  to equilibrium?

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• Problem 3 (44444 points)

• A hot-air balloon stays aloft because hot air at
  atmospheric pressure is less dense than
• cooler air at the same pressure. If the volume of
  the balloon is V500 m3 and the surrounding
• air is at T15.0oC, you will find the temperature
  of the air in the balloon be for it to lift a
  total
• load m290 kg (in addition to the mass of the hot
  air). The density of air at T15.0oC and
• atmospheric pressure is r 1.23 kg/m3. Ignore
  the weight of balloons skin. Answer the
• following questions
• Find the buoyant force B by the air in the
  atmosphere in terms of V, r and g?
• What must the density of the hot air r be for
  the balloon and the load to float in the
  atmosphere in terms V, r, and m?
• From the ideal gas equation pVnRT, derive the
  relation rT constant at a constant pressure.
• If the temperature of the hot air is T, express
  T by T, r, and r.
• Express T in terms of T, r, m and V.
• Plug-in all the numerical values needed and find
  the temperature of the hot air.