Question

Nitrogen is sometimes bubbled into fermenters to maintain anaerobic conditions. It does not react, and leaves in the fermenter off-gas. However, it can strip water from the fermenter so that water vapor also leaves in the off-gas. In a continuous fermenter operated at 33 oC, 20 g h1 water is evaporated in this way. How much heat must be put into the system to compensate for evaporative cooling and so maintain the temperature at a constant value?

Answer 1

In evaporation, we know that some part of liquid phase is converted into vapor phase. Please note that energy of the system has to be conserved so whatever heat is required in vaporization, it comes from sensible heat of the system. If we do not provide a compensation for this heat loss, system temperature may start to reduce

Now in our case it is stated in the problem that temperature of the system is not falling which means whatever heat is utilized in evaporation, needs to be compensated from external source to maintain the temperature.

Now temperature is 33 Degc of the system So heat lost in vaporization would be latent heat of vaporization corresponding to 33 degc of saturation temperature.

From steam table, latent heat of vaporization at 33 deg c=2422.7 kJ/kg

Now for weight of 20g/hr or 0.02 kg/hr, total heat of vaporization = .02*2422.7 = 48.45 KJ/Hr.

Thus heat required to compensate for evaporative cooling = 48.45 KJ/Hr