if incoming water is 12 C and you need to raise it to 42 C, what is the maximum amount of water we can heat with a power source delivering 200 kW/hour?

Question

if incoming water is 12 C and you need to raise it to 42 C, what is the maximum amount of water we can heat with a power source delivering  200 kW/hour?

jamesj · Answer

I just edited the question to make it clearer.   A question however: a power source is rated in Watts.  So is it the power source is 200 kW.  Or is it we have 200 kW.hours of energy?

anonymous · Answer

it should be energy so as to use that to convert it to heat energy......

jamesj · Answer

In other words, 200 kW/hour makes no sense.  It has to be either 200 kW or 200kW.hours.  @ciaran: which is it?

jamesj · Answer

We can conceive the question of "what is the amount of water we can raise from 12 C to 42 C with 200 kW.hours of energy?"
or
"What is the amount of water per hour we can raise from 12 C to 42 C with 200 kW of power?"

Which of these two is it?

jamesj · Answer

@ciaran, please clarify the question.

anonymous · Answer

Let the maximum amount of water that can be heated per hour is m.
$$Q=m \times s \times \Delta T$$...(i)
$$\Delta Q= 200 \times 1$$....(ii)
from (i) and (ii) find m...

anonymous · Answer

in (i) replace Q by $$\Delta Q$$... that's mistake. and compare (i) and (ii)

anonymous · Answer

No. @Taufique please check your units. @JamesJ brings about valid points here. 

First, note that$$Q {[\rm J]} = m {\rm [kg]} \cdot c_p \left[ \rm kJ \over kg \cdot K \right] \cdot \Delta T {\rm [K]}$$where a Joule is of units of energy. 

Now, if the power plant is rated in terms of kW  (one of the two options JamesJ presents)$$\dot Q {\rm \left[W ~ or ~ {J \over s}\right ]} = \dot m \left [ \rm kg \over s \right] \cdot c_p \left [\rm kJ \over kg \cdot K \right] \cdot \Delta T {\rm [K]}$$

Since the power plant is rated in kW/hour, we have an imaginary unit of$$\rm energy \over time^2$$I can conceive no way to manipulate the above equation to match these units. 

In JamesJ's second case (kW*hour), we have units of Joules.

anonymous · Answer

@ciaran If you desire an answer, you need to clarify the units on the  power source.

anonymous · Answer

@eashmore ,here time is not given ,hence we can find only the amount of water in kg/time unit.