How much energy is released by 10 kg of liquid silver at 961°C as it cools to solid silver at 20°C?
To calculate the amount of energy released during the cooling process, we will need to use the heat capacity of silver. The heat capacity is a measure of how much heat energy is required to raise the temperature of a substance.
The specific heat capacity of silver is 0.235 J/g°C. However, to calculate the energy released, we need to convert the mass of the liquid silver from kilograms to grams. Therefore, we multiply the mass (10 kg) by 1000 to convert it to grams, which gives us 10,000 grams.
Now, we can use the formula:
q = m × c × ΔT
Where:
q is the amount of heat energy released (in Joules),
m is the mass of the silver (in grams),
c is the specific heat capacity of silver (in J/g°C),
ΔT is the change in temperature (in °C).
The initial temperature (T1) is 961°C, and the final temperature (T2) is 20°C. Therefore, the change in temperature (ΔT) is T2 - T1 = 20°C - 961°C = -941°C.
Substituting the values into the formula, we get:
q = 10,000 g × 0.235 J/g°C × (-941°C)
Calculating this, we find:
q ≈ -219,535,000 J
Therefore, approximately -219,535,000 Joules of energy are released as the 10 kg of liquid silver cools to solid silver. The negative sign indicates that energy is being released, as the system (silver) is losing heat.