an ideal refrigerator-freezer operates with a COP=7.0 in a 25 degree room. what is the temperature inside the freezer?
To find the temperature inside the freezer, we need to use the equation for the coefficient of performance (COP) of a refrigerator. The COP is defined as the ratio of the heat removed from the cold space (the freezer) to the work input.
COP = Heat Removed / Work Input
In this case, the COP is given as 7.0, which means for every unit of work input, the refrigerator removes 7 units of heat from the freezer.
Now, let's assume the temperature inside the freezer is T. The heat removed from the cold space is equal to the heat absorbed by the refrigerator, which is given by the equation:
Heat Removed = Refrigeration Effect = mcΔT
where:
m = mass of the substance in the freezer
c = specific heat capacity of the substance
ΔT = change in temperature
Since the specific heat capacity and mass are constant, the COP can be written as:
COP = mcΔT / Work Input
Replacing the COP value given (7.0), we have:
7.0 = mcΔT / Work Input
Now, we know that Work Input = mcΔT + Power consumed by the refrigerator.
Assuming the power consumed by the refrigerator is negligible compared to the work input, we can simplify the equation to:
Work Input ≈ mcΔT
Substituting this back into the COP equation, we get:
7.0 = mcΔT / (mcΔT)
7.0 = 1 / ΔT
Now, solve for ΔT:
ΔT = 1 / 7.0
Therefore, the change in temperature inside the freezer is approximately equal to 1/7.0, which is 0.14285714 degrees.
Hence, the temperature inside the freezer is reduced by approximately 0.143 degrees.
COP= ti/(Ts-ti)= ti/(298-ti)
solve for ti.
I get around -10C