Final answer:
The specific heat of the metal is calculated using the formula for heat transfer (q = mcΔT). With 8250 J of heat absorbed, a mass of 5 kg, and a temperature change of 15 °C, the specific heat is found to be 110 J/kg°C.
Step-by-step explanation:
To calculate the specific heat of a metal when given the mass, the amount of heat absorbed, and the change in temperature, you can use the formula:
q = mcΔT
Where:
q is the heat absorbed (in Joules),
m is the mass of the substance (in kilograms),
c is the specific heat capacity (in J/kg°C),
ΔT is the change in temperature (in °C).
Rearranging the formula to solve for c gives:
c = q / (mΔT)
Given q = 8250 J, m = 5 kg, and ΔT = 15 °C, we can plug these values into the formula:
c = 8250 J / (5 kg * 15 °C) = 8250 J / (75 kg°C) = 110 J/kg°C
The specific heat of the metal is 110 J/kg°C.