Question

2. The Rhett Butler Peach, Co. dips the peaches in boiling water (100 degrees Celsius) to remove the skin (a process known as blanching) before canning them. The wastewater from the process is high in organic matter and it must be treated prior to disposal. The treatment process is a biological process that operates at 20 degrees Celsius. Thus, the wastewater must be cooled to 20 degrees before disposal. Forty cubic meters of wastewater is discharged to a concrete tank at a temperature of 20 degrees Celsius to allow to cool. Assuming no losses to the surroundings and that the concreate tank has a mass of 42,000 kg and a specific heat of 0.93kj/kgK. What is the equilibrium temperature of the concrete tank and the wastewater.

Answer 1

Ans) Given,

Treatment temperature = 20 C

Volume of wastewater = 40 m³

Mass of concrete tank = 42000 kg

Specific heat = 0.93 kJ/kg K

We know, density of water = 1000 kg/m³ , hence the loss in enthalpy of boiling water is,

$\Delta$ H = Density x volume x specific heat of water x ( 373.15 - T)

where , absolute temperature is 373.15 K ( 100 + 273.15)

  $\Delta$H = 1000 x 4.186 x (373.15 - T)

Gain in enthalpy of concrete tank is ,

$\Delta$H = mass x specific heat x (T - 293.15)   

$\Delta$H = 4200 x 0.93 x (T - 293.15)

At equilibrium, enthalpy of concrete = enthalpy of water,

4186 x (373.15 - T) = 3906 (T - 293.15)

On solving, T = 358 K

or (358 - 273) = 85^o C