Thermmodynamics!!?

Question

A flow at the rate of 600 lbm/h of hot air at 1 atm and 1500 deg F mixes adiabatically with 120 lbm/h of ambient air at 1 atm and 70 deg F. The mean specific heat at constant pressure for air in this temperature range can be taken as 0.26 Btu/lbm*deg R. Determine for the mixed air steam

(a) the mas flow rate in lbm/h

(b) the temperature in deg F

How do you set this type of problem up? i am not understanding this material!

thanks for you help!

Answer 1

Ah, thermogoddamnics... a class which I struggled in but which gave me so much.

The mass-flow is simple; you have 600 lbm/hr hot and 120 lbm/hr ambient, for a total of 720 lbm/hr.

The product temperature is harder.  You need to multiply the mass-flow ratio by the specific heat and temperature to get the total energy in BTU, then divide by the total mass flow times specific heat:

          T1m1c1 + T2m2c2

Tout = ----------------------

          m1c1 + m2c2

Since the specific heats are all the same (c1 = c2 = c), they fall out of the equation as a unity multiplier and you're left with this:

          T1m1 + T2m2

Tout = ----------------------

          m1 + m2

All you're doing is adding the total heat energy relative to the (arbitrary) zero point, then dividing by the total heat capacity to get the temperature relative to the zero point.  This isn't any different than adding weights times arms to get moments, then dividing by mass to get the center of gravity.

Answer 2

From the back of my head, I would find the enthalpies for both fluids. (Hot air and ambient air). You may find this data from your thermodynamic tables from the appendix of your book. Remember that enthalpies (h) are gathered with pressure and temperatures. Hint: Air at 1500 ºF is superheated. You have flow rates for both fluids and Cp. (Cp=specific heat).

I took thermo sometime ago so I may be a little rusty. But with the given flowrates and the enthalpies you can stabilish a difference that will give you as a result the resultant mass flow. Also take into account that this fluid undergoes an adiabatic expansion which means that there is no heat generated (Q=0). This fact may help you with the temperature in ºF. When there is no heat generated that means that the total temp. will not exceed 1500ºF.

Hope this gives you an idea at least.