When to Use m*cp*del t vs. m*del H

[GR8 PLUMENG]

Is there specific situation when m*cp*del T is not advised when solving problems? I did a few problems and gotte them wrong when I used this formula, especially when dealing with air. 

Any input will be appreciated. 

 

[ME_VT_PE]

I believe constant specific heats can be used unless you're told to use variable specific heats. You would then use the low pressure air tables. Many problems involving adiabatic efficiency require the use of the low pressure air tables, relative pressures, and variable specific heats.

 

[Slay the P.E.]

Is there specific situation when m*cp*del T is not advised when solving problems? I did a few problems and gotte them wrong when I used this formula, especially when dealing with air. 

Any input will be appreciated. 

If you use the “wrong” value of cp you’re going to get it “wrong”. You can always get accurate results with cp*[SIZE=11.0pt]Δ[/SIZE]T if you use the “right” cp.

For example, if you have air going from 800°F to 810°F, but you use the value of cp at 70°F you will be “wrong” i.e., off by a few percent. So, even here when there is small [SIZE=11.0pt]Δ[/SIZE]T (and cp in that range is pretty darn constant) you will be wrong for using the wrong value. Note: For 800°F to 810°F, cp=0.257 Btu/lbm/F while for 70F cp=0.24  Btu/lbm/°F -- a difference of about 7%

Another example; If you have air going from 70°F to say, 1000°F and use cp evaluated at 70°F (or at 1000°F) your results will be less accurate than if you use cp evaluated at the average temperature of roughly 540°F, which is 0.249 Btu/lbm/F (or if you use the average of the cp values evaluated at 70°F and at 1000°F)

Some problems, however, explicitly  ask you to use the “cold-air standard”. What specific problem did you get wrong by assuming constant cp? I’m curious now.

 

[GR8 PLUMENG]

If you use the “wrong” value of cp you’re going to get it “wrong”. You can always get accurate results with cp*[SIZE=11pt]Δ[/SIZE]T if you use the “right” cp.

For example, if you have air going from 800°F to 810°F, but you use the value of cp at 70°F you will be “wrong” i.e., off by a few percent. So, even here when there is small [SIZE=11pt]Δ[/SIZE]T (and cp in that range is pretty darn constant) you will be wrong for using the wrong value. Note: For 800°F to 810°F, cp=0.257 Btu/lbm/F while for 70F cp=0.24  Btu/lbm/°F -- a difference of about 7%

Another example; If you have air going from 70°F to say, 1000°F and use cp evaluated at 70°F (or at 1000°F) your results will be less accurate than if you use cp evaluated at the average temperature of roughly 540°F, which is 0.249 Btu/lbm/F (or if you use the average of the cp values evaluated at 70°F and at 1000°F)

Some problems, however, explicitly  ask you to use the “cold-air standard”. What specific problem did you get wrong by assuming constant cp? I’m curious now.

Sorry for the really late reply.

HVAC 6 min solution number 52 is similar to what am confused about. They used Cp delta T for the water side. I used m*hfg and the results are incorrect.

Please explain if possible.

 

[Slay the P.E.]

In the water side of the heat exchanger in that problem, the fluid remains liquid at all times, therefore using h_fg as the specific enthalpy change would be incorrect. Only when you have phase change from saturated liquid to saturated vapor (or vice-versa) is the enthalpy change per unit mass equal to h_fg.

 

[GR8 PLUMENG]

Ohhhhhh. Thanks for the explanation. That makes lots of sense. Really appreciate it.