A crude fermenter is set up in a shed in the backyard of a suburban house. Under anaerobic conditions with ammonia (NH3) as nitrogen source, about 0.45 g ethanol (C2HsO, MW 46.1) are formed per g glucose (C6H1206, MW 180.2) consumed. At steady state, the production rate of ethanol averages 0.4 kg/h. The owner of this enterprise decided to reduce his electric bill by using the heat released during the fermentation to warm water as an adjunct to the household hot water system. 2.5 L/h cold water at 10°C is fed into a jacket surrounding the fermenter.

To what temperature is the water heated?

Heat losses from the system are negligible. Use a biomass composition of CH17500 58N018 plus 8% ash. The stoichiometric equation is as:
C6H12O6 + b NH3 ---> c (CH1.75N0.18O0.58) + d CO2 + e H2O + f C2H6O

The heats of combustion (Δhe°) for various products are as:
ΔHc for glucose =-2805 kJ/gmol
ΔHc for NH3 = -382.6 kJ/gmol
ΔHc for biomass=-21.2 kJ/gmol
ΔHc for ethanol =-1366. kJ/gmol
Density of water = 1 kg/L, specific heat of water = 75.4 J/(gmol. °C), MW of water = 18