A heat exchanger is considered to recover heat from the exhaust air of a 5,000-cfm laboratory makeup air system located in Denver, Colorado. The indoor temperature within the laboratory is kept at T_in = 70°F. The exhaust air temperature is T_ea = 120°F.

a. Estimate the amount of outdoor air that needs to bypass the heat recovery system under winter design conditions (Toa = −10°F) to ensure that the supply air temperature is equal to the indoor temperature (i.e., T_sa = T_in).

b. Determine the simple payback period if the installation cost of the heat recovery system is $1/cfm. For Denver, the average winter season outdoor temperature is T_oa = 42.4 °F and the cost of gas is $0.10/CCF. The heat recovery system is operated 24 hours/day, 271 days/year (winter season). The heat content of gas is 840 Btu/ft3 (Denver is located at an altitude of about 5,280 ft).