Question

Steam enters a counterflow heat exchanger operating at steady state at 0.06mpa with a quality of 0.9 and exits at the same pressure as saturated liquid. The steam mass flow rate is 1.5kg/min. A separate stream of air with a mass flow rate of 100kg/min enters at 30°C and exits at 60°C. What is the temperature change of the air in the heat exchanger?

1) 30°C
2) 40°C
3) 50°C
4) 60°C

Answer 1

The temperature change of the air in the heat exchanger is 337.312°C.

Step-by-step explanation:

The temperature change of the air in the heat exchanger can be determined using the energy balance equation:

Energy in = Energy out

For the air stream:

Energy in = mcΔT

where m is the mass flow rate of the air, c is the specific heat capacity of air, and ΔT is the temperature change of the air.

For the steam stream:

Energy out = mLh

where m is the mass flow rate of the steam and Lh is the latent heat of vaporization of steam.

Since the heat exchanger is operating at steady state, the heat transfer is equal between the two streams:

mcΔT = mLh

Solving for ΔT:

ΔT = \(\frac{mL_h}{mc}\)

Plugging in the given values:

ΔT = \(\frac{1.5 \times 2256 \times 10^3}{100 \times 1.005}\) = 337.312°C

Therefore, the temperature change of the air in the heat exchanger is 337.312°C.