Compare the amount of heat required to change the temperature of 150 kg of copper from 12 degrees celcius to 56 degrees celcius to the amount of heat required to change the temperature of 150 kg of gold from 12 degrees celcius to 56 degees celcius.
To compare the amount of heat required to change the temperature of copper and gold from 12 degrees Celsius to 56 degrees Celsius, you need to use the specific heat capacity formula:
Q = mcΔT
Where:
Q is the amount of heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, you need to find the specific heat capacity values for copper and gold. The specific heat capacities of copper and gold are as follows:
Copper: 0.385 J/g°C
Gold: 0.129 J/g°C
Note: The specific heat capacity is typically given in units of J/g°C (Joules per gram per degree Celsius). However, since we are dealing with kg of material, we will need to convert the mass and specific heat capacity units to match.
Let's perform the calculations:
For copper:
Mass of copper = 150 kg
Specific heat capacity of copper = 0.385 J/g°C
Converting mass to grams:
Mass of copper = 150 kg * 1000 g/kg = 150,000 g
Calculating the heat required:
Q(copper) = (mass of copper) * (specific heat capacity of copper) * (ΔT)
= 150,000 g * 0.385 J/g°C * (56°C - 12°C)
= 150,000 g * 0.385 J/g°C * 44°C
= 2,508,000 J
For gold:
Mass of gold = 150 kg
Specific heat capacity of gold = 0.129 J/g°C
Converting mass to grams:
Mass of gold = 150 kg * 1000 g/kg = 150,000 g
Calculating the heat required:
Q(gold) = (mass of gold) * (specific heat capacity of gold) * (ΔT)
= 150,000 g * 0.129 J/g°C * (56°C - 12°C)
= 150,000 g * 0.129 J/g°C * 44°C
= 961,920 J
Therefore, the amount of heat required to change the temperature of 150 kg of copper from 12°C to 56°C is 2,508,000 J, while the amount of heat required to change the temperature of 150 kg of gold from 12°C to 56°C is 961,920 J.
In conclusion, it requires more heat to change the temperature of copper compared to gold, given the same mass and temperature change.