To calculate the amount of heat energy needed to cause the rise in temperature, we will use the formula:
Q = m * c * ΔT
Where:
Q is the heat energy (in joules)
m is the mass of the water (in grams)
c is the specific heat capacity of water (in joules/gram°C)
ΔT is the change in temperature (in °C)
In this case:
m = 100 grams
c = 4.18 joules/gram°C
ΔT = 37°C - 4°C = 33°C
Now, we can plug these values into the formula to calculate the heat energy:
Q = 100 grams * 4.18 joules/gram°C * 33°C
Q = 13827 joules
Therefore, the amount of heat energy needed to raise the temperature of 100 grams of water from 4.0°C to 37.0°C is 13,827 joules.