# Thermodynamics solution, but why Cp*1000 ?

1. Nov 6, 2013

### psilocybin

Hi there! I have attached an example problem from my thermodynamics text book, and I understand everything except part (c)

m( h + ke ) = m(c p T + V^2/2)
where Cp is multiplied by 1000 (or ke/1000 as shown in solution.)

why is this part done? I cannot figure it out at all. I see that it is to get the answer in terms of watts rather than kW, but I feel like I am missing something conceptually. In the following step when KE is ignored, it is not done...

Any clarification would be greatly appreciated. Thanks!

Heres the original question if additional context is needed:

Air flows steadily in a pipe at 300 kPa, 77°C, and
25 m/s at a rate of 18 kg/min. Determine (a) the diameter of
the pipe, (b) the rate of flow energy, (c) the rate of energy
transport by mass, and (d ) the error involved in part (c) if the
kinetic energy is neglected.

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2. Nov 6, 2013

### cepheid

Staff Emeritus
Cp is not multiplied by 1000 anywhere, so I don't know where you're getting that.

The last factor in parentheses in the second term is just a unit conversion. Here are two equivalent ways of explaining it.

1. The first term is in kJ/kg, which when multiplied by kg/s gives you kJ/s, or kW. These are the units you want your answer to be in. However, the second term, which is in m^2/s^2, when multiplied by kg/s, gives you J/s, or W, which is not the same. To express the second term in kJ/s rather than J/s, you have to divide it by 1000.

2. You'll notice that the first term is in kJ/kg, which when multiplied by kg/s gives you kJ/s. So, you want the second term to be in kJ/kg as well. Recall that [energy]/[mass] = [speed]^2. The second term is in m^2/s^2. To express this in kJ/kg, we need the conversion factor, which is that 1 kJ/kg = 1000 m^2/s^2. This makes sense, since 1 J/kg = 1 m^2/s^2.

3. Nov 6, 2013

### psilocybin

Thanks, in an alternate handwritten solution it was written with Cp*1000 which started the confusion. The last couple sentences really summed it up. Unfortunately this class has mostly been taught as a "plug these numbers from the table into these formulas" and alot of the intuition has been lost. Thank you for the assistance!