Which needs more energy: to heat 5 kg of copper from 20 degrees celcius to 50 degrees celcius or to heat 0.5 kg of water from 20 degrees celcius to 50 degrees celcius?
To determine which one requires more energy, we need to calculate the amount of heat energy required for each substance using the specific heat capacity formula:
Q = m * c * ΔT
where:
Q is the amount of heat energy (in Joules),
m is the mass of the substance (in kilograms),
c is the specific heat capacity of the substance (in Joules per kilogram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
First, let's calculate the amount of heat energy required to heat the copper:
Given:
m(copper) = 5 kg
c(copper) = 385 J/kg°C (specific heat capacity of copper)
ΔT(copper) = 50°C - 20°C = 30°C
Using the formula: Q(copper) = m(copper) * c(copper) * ΔT(copper)
Q(copper) = 5 kg * 385 J/kg°C * 30°C
Q(copper) = 57750 J
Now, let's calculate the amount of heat energy required to heat the water:
Given:
m(water) = 0.5 kg
c(water) = 4186 J/kg°C (specific heat capacity of water)
ΔT(water) = 50°C - 20°C = 30°C
Using the formula: Q(water) = m(water) * c(water) * ΔT(water)
Q(water) = 0.5 kg * 4186 J/kg°C * 30°C
Q(water) = 62790 J
Comparing the values we calculated, we find that it takes more energy to heat 0.5 kg of water from 20°C to 50°C (62790 J) than to heat 5 kg of copper from 20°C to 50°C (57750 J). Therefore, heating 0.5 kg of water requires more energy.