(a) what is the best coefficient of performance for a refrigerator that cools an environment at −30.0ºc and has heat transfer to another environment at 45.0ºc ? (b) how much work in joules must be done for a heat transfer of 4186 kj from the cold environment? (c) what is the cost of doing this if the work costs 10.0 cents per 3.60×106j (a kilowatt-hour)?

a) 3.242

b) 1291.178 KJ

c) 3.59 cents

Explanation:

a) First all the temperature units should be in Kelvin. -30°C + 273.15 = 243.15K and 45°C + 273.15 = 318.15K. Coefficient of performance for refrigerator is COP = TL/(TH-TL) where TL is Lower Temperature and TH is the Higher Temperature. COP = 243.15/(318.15-243.15) = 3.242

b) COP  = Cooling Effect/Work Input. Cooling Effect (or Desired Output) is 4186 kJ.

So Work Input = Cooling Effect/COP = 4186KJ/3.242= 1291.178 KJ

c) 3.6 MJ (3600kJ) is for 10 cents, using ratio for cost: energy used

3.59 cents

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force