1) One kilogram of ice at 0 deg.Celsius is in a well-insulted container. At t=0,

Question

1) One kilogram of ice at 0 deg.Celsius is in a well-insulted container. At t=0, water at 25 deg.Celsius flows into the container at 0.01kg/s. Assume that the water/ice mixture in the container is always at the equilibrium. To within 0.1s, how long will it take for the ice to be completely melted? How much water was added to achieve this? Note for an incompressible fluid at constant pressure, delta h= delta u= c*delta T, where c is the heat capacity of water, delta h is the change of enthalpy and delta u is the change of internal energy

2) A hydroelectric plant operates at a flow rate of 100m^3/s. The water inlet is at atmospheric pressure and the outlet, 100m below the inlet, is also. As a result of the motion of the turbines, the water temperature increases by 0.25deg.Celsius. What is the work output of the turbine?

Explanation / Answer

1)heat of fusion for ice =333.55 kJ/kg

Ice melts at 0 C

Heat taken for ice to melts=333.55 kJ

Water used for melting ice

mCp(25-0)=333.55

m=333.55/(4.2*25)=3.17 kg

water flow rate=0.01kg/s

time taken to melt the ice completely=3.17/0.01=317s

2)water flow rate=100m3/s=

Potential energy of water=mgh=9.8*104kJ

Energy used in temp increase=105*4.18*0.25=1.05*105kJ

Question seems to be worng as potential energy is less than heat dissipated by turbine

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