# Energy Storage in Heated Water - kWh

## Thermal energy stored in heated water

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Water is often used to store thermal energy. Energy stored - or available - in hot water can be calculated

E = c_{p}dt m (1)

where

E = energy (kJ, Btu)

c_{p}= specific heat of water (kJ/kg^{o}C,Btu/lb^{ o}F) (4.2 kJ/kg^{o}C, 1 Btu/lb_{m}^{o}F for water)

dt = temperature difference between the hot water and the surroundings (^{o}C,^{o}F))

m = mass of water (kg, lb_{m})

### Example - Energy stored in a *1000 liter* water tank

Water is heated to *90 ^{o}C. *The surrounding temperature (where the energy can be transferred to) is

*20*

^{o}C.The energy stored in the water tank can be calculated as

E = (4.2 kJ/kg^{o}C) ((90^{o}C) - (20^{o}C)) (1000 liter) (1 kg/liter)

= 294000 kJ

= (294000 kWs) (1/3600 h/s)

= 81.7 kWh

*1 J (Joule) = 0,1020 kpm = 2.778x10*^{-7}kWh = 2.389x10^{-4}kcal = 0.7376 ft lb_{f}= 1 (kg m^{2})/s^{2}= 1 watt second = 1 Nm = 1 ft lb = 9.478x10^{-4}Btu*1 Btu (British thermal unit) = 1055.06 J = 107.6 kpm = 2.92875x10*^{-4}kWh = 251.996 calorie (IT - International Table calorie) = 0.252 kcal = 777.649

### Example - Solar Energy stored in a *200 US gallons* Water Tank

A solar energy water buffer tank with* 200 US* gallons is heated *200 ^{o}F. *

The solar energy stored can be calculated as

E = (1 Btu/lb) (200_{m}^{o}F^{o}F) (200 US gallons) (8.3 lb_{m}/US gallon)

= 332000 Btu

### Energy Stored in Water - Liters/kWh

### Energy Stored in Water - US gallons/Btu's

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