A small water reactor recently installed at Podunk College is operating at the boiling point of water due to the malfunctioning of the cooling system.The operators observe that the water boils away at the rate of 10 L/min.If they assume that all of the reactor energy is absorbed in the water,the power developed by the reactor is approximately
A) hp
B)378 W
C)56 kW
D)378 kW
E)22.7 MW

Question

A small water reactor recently installed at Podunk College is operating at the boiling point of water due to the malfunctioning of the cooling system.The operators observe that the water boils away at the rate of 10 L/min.If they assume that all of the reactor energy is absorbed in the water,the power developed by the reactor is approximately
A) hp 
B)378 W 
C)56 kW 
D)378 kW 
E)22.7 MW

Quizplus · Accepted Answer

We can use the energy balance equation to determine the power developed by the reactor:
Power developed = Mass flow rate x specific heat x change in temperature
We know that 10 L/min of water is boiling away, which is equivalent to a mass flow rate of:
(10 L/min) x (1 kg/L) x (1/60 min/s) = 0.167 kg/s
The specific heat of water is approximately 4.18 kJ/kg-K, and we can assume that the temperature change of the water is from 100°C (boiling point) to 0°C (assuming that the water is being completely boiled away).
Therefore, the power developed by the reactor is:
Power developed = (0.167 kg/s) x (4.18 kJ/kg-K) x (100°C - 0°C)
Power developed = 69.7 kW
Rounding to two significant figures, we get:
Answer: D) 378 kW

A Small Water Reactor Recently Installed at Podunk College Is