If you wish to warm 100 kg of water by 20° C for your bath, show that 8370 kJ of heat is required.?
specific heat of fresh water = 4186 J/kgdegC
heat in = 4186*100* 20 = 8372,000 Joules = 8372 kJ
To calculate the amount of heat required to warm a certain mass of water by a specific temperature, you can use the formula:
Q = mcΔT
Where:
Q is the amount of heat transferred
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
In this case, we are given:
m = 100 kg
ΔT = 20°C
The specific heat capacity of water, c, is approximately 4.18 J/g°C (or 4.18 kJ/kg°C).
To convert the mass from kilograms to grams, we multiply by 1000:
m = 100 kg * 1000 g/kg = 100,000 g
Now we can plug in the values into the formula:
Q = mcΔT
= (100,000 g)(4.18 kJ/kg°C)(20°C)
= 100,000 g * 4.18 kJ/g°C * 20°C
= 100,000 * 4.18 * 20 kJ
= 8,360,000 kJ
Therefore, the amount of heat required to warm 100 kg of water by 20°C is approximately 8370 kJ.