What is the maximal coefficient of performance of a refrigerator which cools down 10 kg of water (and then ice) to -6C. Upper he
1 answer:
Given:
Temperature of water, =
=273 +(-6) =267 K
Temperature surrounding refrigerator, =
=273 + 21 =294 K
Specific heat given for water, = 4.19 KJ/kg/K
Specific heat given for ice, = 2.1 KJ/kg/K
Latent heat of fusion, = 335KJ/kg
Solution:
Coefficient of Performance (COP) for refrigerator is given by:
Max =
= = 9.89
Coefficient of Performance (COP) for heat pump is given by:
Max =
= 10.89
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Assumptions:
- Steady state.
- Air as working fluid.
- Ideal gas.
- Reversible process.
- Ideal Otto Cycle.
Explanation:
Otto cycle is a thermodynamic cycle widely used in automobile engines, in which an amount of gas (air) experiences changes of pressure, temperature, volume, addition of heat, and removal of heat. The cycle is composed by (following the P-V diagram):
- Intake <em>0-1</em>: the mass of working fluid is drawn into the piston at a constant pressure.
- Adiabatic compression <em>1-2</em>: the mass of working fluid is compressed isentropically from State 1 to State 2 through compression ratio (r).
- Ignition 2-3: the volume remains constant while heat is added to the mass of gas.
- Expansion 3-4: the working fluid does work on the piston due to the high pressure within it, thus the working fluid reaches the maximum volume through the compression ratio.
- Heat Rejection 4-1: heat is removed from the working fluid as the pressure drops instantaneously.
- Exhaust 1-0: the working fluid is vented to the atmosphere.
If the system produces enough work, the automobile and its occupants will propel. On the other hand, the efficiency of the Otto Cycle is defined as follows:
where:
Ideal air is the working fluid, as stated before, for which its specific heat ratio can be considered constant.
Answer:
See image attached.
