Suppose you want to heat 40 kg of water by 20 C. How many joules of heat are required?
q = mcdelta T
q = 40 x 1000 x 4.184 x 20
To calculate the amount of heat required, we can use the formula:
Q = m * c * ΔT
Where:
Q = Amount of heat (in joules)
m = Mass of water (in kilograms)
c = Specific heat capacity of water (in joules per kilogram per degree Celsius)
ΔT = Change in temperature (in degrees Celsius)
In this case, we are given:
m = 40 kg (mass of water)
ΔT = 20 °C (change in temperature)
The specific heat capacity of water is approximately 4.186 J/g·°C (joules per gram per degree Celsius), or 4186 J/kg·°C (joules per kilogram per degree Celsius).
Now, we need to convert the mass of water from kilograms to grams because the specific heat capacity is given in joules per gram per degree Celsius.
Mass (in grams) = 40 kg * 1000 g/kg = 40000 g
Now we can substitute the given values into the formula:
Q = 40000 g * 4186 J/kg·°C * 20 °C
Q = 836,800,000 joules
Therefore, to heat 40 kg of water by 20 °C, 836,800,000 joules of heat are required.