Country livin\' is hard. Prof L lives with his wife, dogs, and goats on a mini f
ID: 1778702 • Letter: C
Question
Country livin' is hard. Prof L lives with his wife, dogs, and goats on a mini farm in Southern Chester County, PA. (True story.) Last year, the power went out for an extended period of time in winter, and Prof L decided to make a hot bath the old school way, since his house was built in 1798. (Made that part up.) In a large tube, he heated 50 liters of water to 55 °C over a fire, and then added 25 liters of cold water at 10 °C.
(a) What was the temperature of the tub after mixing the water?
(b) What was the change in entropy as a result of this process?
Explanation / Answer
Consider this question like adding two streams of water in a tub.
Stream 1 is that of water at 55 degree Celsius
Stream 2 is that of water at 10 degree Celsius
a)Let the final temperature of both streams be T
Then applying heat balance
m1Cp(T-55)+m2Cp(T-10)=0
Density of water can be assumed as 1 kg per litre
Solving the equation
We get T=40 degree Celsius
b) As we know at constant pressure
dS=CpdT/T
Hence total entropy change=dS1+dS2
dS1=4.186*ln(40/55)
dS2=4.186*ln(40/10)
Solving dS=4.4699 kJ/kg