Water enters a baseboard radiator at 180 °F and at a flow rate of 2.0 gpm. Assuming the radiator releases heat into the room at a rate of 20,000 Btu / hr., what is the temperature of the water leaving the radiator?

Temperature of water leaving the radiator = 160°F

Explanation:

Heat released = (ṁcΔT)

Heat released = 20000 btu/hr = 5861.42 W

ṁ = mass flowrate = density * volumetric flow rate

Volumetric flowrate = 2 gallons/min = 0.000126 m³/s; density of water = 1000 kg/m³

ṁ = 1000 * 0.000126 = 0.126 kg/s

c = specific heat capacity for water = 4200 J/kg. K

H = ṁcΔT = 5861.42

ΔT = 5861.42 / (0.126 * 4200) = 11.08 K = 11.08°C

And in change in temperature terms,

10°C = 18°F

11.08°C = 11.08 * 18/10 = 20°F

ΔT = T₁ - T₂

20 = 180 - T₂

T₂ = 160°F