Final answer:
The total amount of heat needed to raise the temperature of 2.25 kg of silver from 0.0°C to 200.0°C is 290,250 joules, calculated using the specific heat capacity of silver and the mass-temperature change formula.
Step-by-step explanation:
To calculate the total amount of heat needed to change 2.25 kg of silver at 0.0°C to 200.0°C, we use the formula for heat transfer Q = mcΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, we convert the mass of silver from kilograms to grams because the specific heat of silver is given in J/g. Since 1 kg = 1000 g:
2.25 kg × 1000 g/kg = 2250 g
The change in temperature (ΔT) is the final temperature minus the initial temperature, which is 200.0°C - 0.0°C = 200.0°C.
Now, we plug in the values into the formula:
Q = (2250 g) × (0.129 J/g°C) × (200.0°C)
Q = 290,250 J
Therefore, the total amount of heat required to raise the temperature of 2.25 kg of silver from 0.0°C to 200.0°C is 290,250 joules.