Final answer:
To find the energy required to raise the temperature of 45 g of copper from 54.8 °C to 89.7 °C, the specific heat capacity formula is used, resulting in an energy requirement of approximately 953.3 joules.
Step-by-step explanation:
To calculate the energy required to raise the temperature of 45 g of copper from 54.8 °C to 89.7 °C, we need to use the specific heat capacity formula:
Q = mcΔT
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 (in J/kg°C), and
- ΔT is the change in temperature (in °C).
First, we convert 45 g of copper to kilograms:
Next, we use the given heat capacity of copper, 38.5 J K-1 mol-1, but since the mass is given in grams, we first need to convert the specific heat capacity to J/kg°C. We also know the molar mass of copper is approximately 63.55 g/mol, so:
- c = 38.5 J K-1 mol-1 * (1 mol / 63.55 g) * (1000 g / 1 kg) = 605.4 J/kg°C
Now we can calculate ΔT:
- ΔT = 89.7 °C - 54.8 °C = 34.9 °C
Finally, we calculate Q:
- Q = 0.045 kg * 605.4 J/kg°C * 34.9 °C = 953.3 J
The energy required to raise the temperature of 45 g of copper from 54.8 °C to 89.7 °C is approximately 953.3 joules.