Wednesday, October 22, 2008

TE 303 - HW #5, P8 - Transient Heating of an Office Space - 18 pts

The air supply to a 20000 ft3 office has been shut off overnight to conserve utilities, and the room temperature has dropped to 40oF. In the morning, a worker resets the thermostat to 70oF, and 200 ft3/min of air at 120oF begins to flow into the office through a heating duct. The air is well-mixed within the room and an equal mass flow of air at room temperature is withdrawn through a return duct. The air pressure is essentially 1 atm everywhere. Ignoring heat exchange with the surroundings, as well as any changes in kinetic or potential energies, estimate how long it takes for the room temperature to reach 70oF. Assume g = 1.4 for the air.

HINTS :
This is a transient or unsteady process because helium enters the system (the balloon). Assume the He behaves as an ideal gas, but check to see if this is a good assumption. Use the IG EOS to determine the initial mass of He in the balloon. After you determine V2, calculating Wb is easy ! Then, simultaneously solve two equations in two unknowns. The equations are: the IG EOS applied to the final state of the balloon and the transient form of the 1st Law applied to this process. The two unknowns are: T2, mHe,2 .
The catch is that we must determine values for U1, U2 and Hin. These are NOT ΔU's and ΔH's but real U's and H's. In order to do this (just like the steam tables) we MUST choose a reference state. A reference state is a T, P and phase at which YOU choose to make EITHER U or H zero kJ/kg. I want you to use a reference state of U = 0 for He gas at 22 oC and 100 kPa. The P doesn't actually matter because He is treated as an IG in this problem so U and H are not functions of P anyway.

Once you have a ref state, use a Hypothetical Process Path from the ref state to states 1, 2 and inlet to evaluate U1, U2 and Hin using the IG EOS and CV and CP given in the problem.

For He, use: CP = 5.1926 kJ/kg-K and CV = 3.1156 kJ/kg-K.

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1 comment:

Anonymous said...

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HINTS:
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* Remember to check out the comments from Dr. B's class

* Assume that the mass of air in the room remains constant as the air in the room heats up. You can evaluate it at the average room temperature of 55 C.

* Assume that the office is adiabatic.

* See the problem description for other hints!!

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ANSWERS:
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m_sys = 1543.3 lbm

t = 37.8 min