# h=cp*deltaT



## Viper5 (Apr 4, 2017)

I am having difficulties knowing when it is acceptable to apply the h=cp*deltaT condition.  I am working through some problems and I can't distinguish why in some cases they just use h.  For instance, one problem expands steam from a turbine with cooling water available and it's setup as (mdot*cp*delta_T)_water = (mdot*delta_h)_steam, yet another problem uses a heat exchanger and (mdot*delta_h)_water to find energy rate. 

As I understand it currently, this substitution for h is permitted when dealing with a perfect gas, but why then is water considered perfect?

I can post questions and solutions, but just trying to find the missing link here.  Thanks.


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## JHW 3d (Apr 4, 2017)

It's an energy balance. Energy in = energy out. Energy can be used to change the temperature of water (sensible heat, using cp * delta-T), or it can be used to change the phase of water vapor (latent heat, using delta-h), or sometimes both. That is the basic idea.


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## Audi Driver P.E. (Apr 4, 2017)

It's going to depend a lot on what is given in the problem, too.  Table values of Cp for gasses are usually only given for 1 atm (unless you're lucky enough to have an expanded table with Cp values in it for various pressures).  Much deviation from that and you can't use it.  Cp is also temperature dependent and state dependent as can be seen from the typical values of ~0.45 Btu/lbm deg. R (which is really only valid for low temperature steam at ~212 deg.F) at atmospheric pressure and ~1.0, which is a good approximation for liquid state water between 32 and 212 (greater pressure variation is allowable, but 1.0 is really only valid for 1 atm).  So, if your steam/water varies widely in temperature and/or pressure, you're going to have to dive into the steam tables and look at h values which are more commonly used in those cases.


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## Viper5 (Apr 4, 2017)

Thanks for the speedy reply.  The sensible vs latent heat definitely makes sense.  It seems it's always safe to use the 'h' variation, but one should be cautious when using cp*delta_T is what I'm getting out of this.


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## Audi Driver P.E. (Apr 4, 2017)

If Cp is a given value in the problem, it's a safe bet that you can use that value, assuming it isn't merely extra information.


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