Please show each step: If you want to heat 100 kg of water at 20 ° C for your bath, calculate the amount of heat in water. Then demonstrate that this is equivalent to 8360 kilojoules.
q needed = mass H2O x specific heat H2O x (Tfinal-Tinitial). I can't calculate anything because you didn't specify the final T of the water.
To calculate the amount of heat in water, we can use the specific heat capacity of water and the formula:
Q = m * c * ΔT
Where:
Q = amount of heat (in joules)
m = mass of the water (in kilograms)
c = specific heat capacity of water (approximately 4.18 joules per gram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
Here are the steps to calculate the amount of heat in water:
Step 1: Convert the mass of water from kilograms to grams.
Since the specific heat capacity of water is given in joules per gram per degree Celsius, we need to convert the mass of water from 100 kg to grams:
100 kg * 1000 = 100,000 grams
Step 2: Calculate the change in temperature.
The change in temperature is the final temperature minus the initial temperature. In this case, we want to heat the water from 20 °C to a higher temperature, but the final temperature is not given. Therefore, let's assume the final temperature as 100 °C (the boiling point of water).
ΔT = final temperature - initial temperature
ΔT = 100 °C - 20 °C
ΔT = 80 °C
Step 3: Substitute the values into the formula.
Q = m * c * ΔT
Q = 100,000 g * 4.18 J/g°C * 80°C
Q = 334,400,000 J
Step 4: Convert joules to kilojoules.
Since the question asks for the amount of heat in kilojoules, we need to convert the units:
334,400,000 J * 0.001 = 334,400 kJ
Therefore, the amount of heat in the 100 kg of water heated from 20 °C to 100 °C is approximately 334,400 kilojoules.
It seems you mentioned that the equivalent amount of heat is 8360 kilojoules. This could be a mistake or there might be some additional information that needs to be considered in order to arrive at that value.