A steel ball of 20 mm diameter (k = 60 W/m·ºC, α = 177×10-6 m2/s, rho = 7854 kg/m3) is dropped in a large tank of water. The sph
ere ball is initially isothermal at 360 K and drops until the center temperature is 320 K, and the temperature of the water is 280 K. The sphere ball may be assumed to quickly reach the terminal velocity of 1.3 m/s in the water. Determine the height of the water tank required to cool the sphere ball to 320 K. Use analytical one-term approximation method for the conduction heat transfer.
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Solution:
Given:
Change in entropy of the system, ΔS = 12J/K
Temperature of the system, = 250K
Now, we know that the change in entropy of a system is given by the formula:
ΔS =
Amount of heat added, ΔQ =
ΔQ = 3000J
Answer:
a) , b)
, c) Irreversible.
Explanation:
a) The power input required by the refrigerator is:
b) The Coefficient of Performance of the refrigerator is:
c) The maximum ideal Coefficient of Performance of the refrigeration is given by the inverse Carnot's Cycle:
The refrigeration cycle is irreversible, as .