How Do You Calculate the Fourth Temperature in a Heat Exchanger?

[baseballer10p]

Homework Statement

I'm given three temperatures and four pressures for a heat exchanger. I am also given the mass flow rate, which is the same for both the inlets and outlets. There is no heat transfer between the heat exchanger and the surroundings. My task is to find the fourth temperature in the heat exchanger. Both fluids are air treated as an ideal gas.

Air1 - (T1 = 610K, P1 = 10^5 Pa, T2 = 860K, P2 = 9.7*10^5 Pa)
Air 2 - (T1 = 1020K, P1 = 1.1*10^5 Pa, P2 = 10^5 Pa, T2 = ?)

Homework Equations

This is what I'm looking for

The Attempt at a Solution

Solving for the fourth temperature:
Air 2

T2 = P2*(T1/P1)

I know this can't be right, but it's all I can think of. I'm drawing a blank on how to find this fourth temperature. Please help!

 

[anathema]

Thank you for sharing your question with us. It seems like you are trying to find the fourth temperature for Air 2 in the heat exchanger. In order to solve this problem, we need to use the ideal gas law and the conservation of energy equation.

First, let's write out the ideal gas law for both Air 1 and Air 2:

PV = mRT

Where P is pressure, V is volume, m is mass, R is the gas constant, and T is temperature.

Since the mass flow rate is the same for both inlets and outlets, we can set the two equations equal to each other:

P1V1 = P2V2

We also know that there is no heat transfer between the heat exchanger and the surroundings, which means that the change in internal energy is equal to zero. This can be written as:

Q = 0 = mCp(T2 - T1)

Where Q is heat transfer, m is mass, Cp is specific heat, and T2 and T1 are the temperatures at the outlets and inlets respectively.

Now we can combine these equations to solve for T2:

P2V2 = P1V1 = mCp(T2 - T1)

Solving for T2, we get:

T2 = T1 + (P1V1)/(mCp)

Finally, we can plug in the values given in the problem to solve for T2:

T2 = 1020K + (1.1*10^5 Pa * V1)/(m * Cp)

I hope this helps you solve your problem. If you have any further questions, please don't hesitate to ask. Good luck!