# Specific heat calculations - How to input the value of the mass when water is flowing through a pipe?

I have been using this specific heat calculator to calculate the energy in joules needed to cause a change in temperature in a mass of water https://www.omnicalculator.com/physics/specific-heat

The calculator requires the following values to be entered -

• The desired change in temperature
• The mass of material being heated
• The specific heat capacity of the material

Suppose I want to heat up the water flowing through the pipe using joule heating to heat the pipe. I know the change in temperature I want to elicit, and I know specific heat capacity of water - how do I calculate the mass?

Say the volume of water in the pipe is 10 cubic mm - however this water is moving. Suppose the flow rate of water through the pipe is 200 cubic millimeters per second. (Hypothetical values of course)

10 divided by 200 = 0.05 seconds for 10 cubic mm to flow through the pipe, so would inputting a mass of 10 cubic mm into the specific heat calculation give an approximate result of the energy in joules needed to heat the water flowing through the pipe for the period of time of 0.05 seconds? (I say approximate result because the water is still moving through the pipe).

I understand that the joules in this calculation are not the real energy required to heat the water. I understand that this calculation may not actually be the right one - or the only one - to use, but I just need to understand this as a starting point. I understand that there are more factors involved in calculating how water is heated, (ambient temperature, heat transfer, laminar vs turbulent flow) but I just want to understand how to estimate the correct mass value in this specific calculation.

It seems to me that if the water is flowing, we must take into account the time that it takes a mass of water to move through the source of heat. It also seems reasonable to assume that the energy required to heat that water is only applicable to the time that the water is in contact with the heat source. Can I then assume that the energy in joules I get from this calculation is for a period of 0.05 seconds?

## 1 Answer

I assume you want to heat a certain mass flow rate of water flowing at steady state, and you want to know the rate at which you need to add heat. Once the system reaches stead state, the mass holdup in the pipe is irrelevant. The rate of heating you need to use is $$\dot{Q}=\dot{m} C\Delta T$$where $$\dot{m}$$ is the mass flow rate of water and C is the heat capacity.

• Thank you Chet Miller. This website mrneave.weebly.com/uploads/1/3/5/9/13590915/… lists the units for that formula as 􏰀 Q = the amount of heat energy lost or gained, (J) 􏰀 m = the mass of the substance, (kg) 􏰀 c = the specific heat capacity of the substance, (J/kg•0C) 􏰀 ΔT = the change in temperature of the substance, (°C) so should I input m as kg? Kg per second? – EddieP Oct 18 '20 at 14:59
• kg/sec and Joules/sec in this flow situation. Doesn't that make sense? – Chet Miller Oct 18 '20 at 15:30
• @EddieP now that you have the formula provided by Chet Miller (in terms of the time rates of change of heat and mass, not heat and mass themselves), you don't need to use the calculator on the website you linked. You can perform the calculation using a handheld calculator, or you could type the formula in a spreadsheet program (Excel or Sheets), where you can vary all the parameters. – electronpusher Oct 18 '20 at 15:47