When we add heat to a substance, its temperature changes based on its specific heat capacity. The specific heat of copper is 0.092 cal/g°C, while the specific heat of silver is 0.057 cal/g°C. This means that copper requires more heat to raise its temperature compared to silver.
Let’s calculate the temperature increase for each metal:
For copper:
Heat added (Q) = 100 cal
Specific heat (c) = 0.092 cal/g°C
Mass (m) = 1 g
Using the formula: Q = mcΔT, we can rearrange this to find ΔT (change in temperature):
ΔT = Q / (mc) = 100 cal / (1 g * 0.092 cal/g°C) ≈ 1087.0 °C
This means the temperature of the copper will rise significantly, reaching approximately 1112 °C.
Now, for silver:
Heat added (Q) = 100 cal
Specific heat (c) = 0.057 cal/g°C
Mass (m) = 1 g
Using the same formula:
ΔT = Q / (mc) = 100 cal / (1 g * 0.057 cal/g°C) ≈ 1754.4 °C
This means the temperature of the silver will rise even higher, reaching approximately 1779 °C.
In conclusion, when we add 100 cal of heat to each metal, the copper will experience a temperature increase of about 1087 °C, while silver will have an increase of approximately 1754 °C, showing that silver heats up more quickly than copper due to its lower specific heat capacity.