Thermal calculations + gas volume calculations

Substance data:	Thermal capacity [kJ/(kgK)]	Density [kg/dm³(litre)]
Water, 20°C	4,1819	0,998234
Water, 100°C	4,216	0,958382
Ethylene glykol (45%)-water	3,33	1,055
Beer wort, 12°P (original wort), 10°C	3,875	1,047
Drinking milk, 2.5% fat, 0°C	3,83	1,0381725
Raw milk, 4.2% fat, 20°C	3,9	1,029484768
Honey, liquid	2,3 - 2,5	~1,4
Sugar, dissolved, 50%, 50°C	3,119	1,215
Sugar, dissolved, 65%, 50°C	2,779	1,302
Sugar, dissolved, 80%, 50°C	2,372	1,396
Olive oil, 25°C	1,858	0,887
Olive oil, 50°C	1,936	0,875
Olive oil, 75°C	2,015	0,863
Ethanol, 50%, 50°C	3,934	0,889
Ethanol, 100%, 50°C	2,718	0,729
For comparison: Aluminium	0,896	2,699

The higher the heat capacity, the more energy is required for heating (compare aluminium).


Example 1 (batch heating):

5000 litres of water are to be heated up from 20°C to 30°C in a container within 30 minutes. The required thermal output must be calculated. An additional 30% must be included for absolute certainty.

- Liquid volume to be tempered: 5000 litres

- Thermal capacity: 4.1819 kJ/kgK

- Temperature difference: 10°K

- Heat loss: 30%

- Density: 0.998234 kg/dm³

- Time: 1800 seconds

Result: P = 151.05 kW

 

Example 2 (continuous "inline" process):

A heat exchanger is to be used to heat a volume flow of 150 hl/hour (1 hl = 100 litres) from 20°C to 30°C. The required thermal output must be calculated. An additional 40% must be included for absolute certainty.

- Volume flow: 15000 litres/h

- Thermal capacity: 4.1819 kJ/kgK

- Temperature difference: 10°K

- Heat loss: 40%

- Density: 0.998234 kg/dm³

- Time: 3600 seconds (as 150 hl flow per hour [3600s])

Result: P = 243.51 kW

Example:

How long does it take to heat a water volume of 5000 litres from 20°C to 30°C if the thermal output of the heater (or the heating surface in the tank wall) is 243 kW? An additional 40% must be included for absolute certainty.

- Volume flow: 5000 litres

- Thermal capacity: 4.1819 kJ/kgK

- Temperature difference: 10°K

- Heat loss: 40%

- Density: 0.998234 kg/dm³

- Heat output: 243 kW

Result: t = 1203 seconds

Substance data:	Heat transfer coefficient* U-value / k-value in kcal/m²h°C
Concrete wall 25mm (not insulated)	2,8
Insulated wall panels (PU foam), 10 cm	0,3
Brick wall 24 cm	1,3
Brick wall 12cm	2,6
Insulated glass windows	2,4
Wooden door (or boarded partition)	3

*= The U values and the earlier k values can be assumed to be identical for
rough estimates

The accompanying calculation programme is based on Richmann's law of mixtures. The mixture temperature can also be determined with the mixture formula given in 1 (in chapter "mixture calculator") if the thermal capacities of the components to be mixed are identical. Both the mixing formula in 1 (in chapter "mixture calculator") and Richmann's law of mixtures can be extended with more components of a mixture than shown here.

m1*c1*(t1-tm) = m2*c2*(tm-t2)

tm = ((m1*c1*t1)+(m2*c2*t2)) / ((m1*c1)+(m2*c2))

Substance data:	Thermal capacity [kJ/(kgK)]
Water, 20°C	4,1819
Water, 100°C	4,216
Ethylene glycol (45%) water	3,33
Beer wort, 12°P (original wort), 10°C	3,875
Drinking milk, 2.5% fat, 0°C	3,83
Raw milk, 4.2% fat, 20°C	3,9

	Warmer liquid	Colder liquid
Mass	m1	m2
Thermal capacity	c1	c2
Temperature	T1	T2