At the START of a day, a lake contains 20,000 kg of liquid water at 25 ?C. The lake, and all water entering or leaving it in any form, has a pressure of 1 bar.

Question

During the course of a day, the following processes affecting the lake occur:

• 200 kg of rain falls into the lake. The rainwater had a temperature of 25 ?C and a velocity of 20 m/sec when it hit the surface of the lake.
• 200 kg of water evaporates from the lake. This water vapor can be assumed to have the same physical properties as saturated vapor at 25 ?C.
• An unknown amount of heat flows into and out of the lake in various forms (solar energy, radiative heat losses, body heat from swimmers, etc.)

Use the following to approximate the physical properties of liquid water:

• For liquid water at T=25 ?C and P=1 bar, the enthalpy and internal energy of water are essentially identical; use 105 kJ/kg for either.
• The heat capacity of liquid water can be considered constant with Cv=Cp=4.2 kJ/kg-C.
• The molar volume of liquid water is 18 cm3/g and is constant with respect to temperature.

A) Write the generalized energy balance equation. Identify and cross out all terms that are insignificant when the energy balance is applied to the lake.
B) If the lake’s temperature is 26 ?C at the end of the day, compute the unknown amount of heat that was added or removed during the day.

Answer 1