A 77.40 kg piece of copper metal is heated from 19.6°C to 337.3°C. Calculate the heat absorbed (in kJ) by the metal.
First you must determine if the Cu goes through a phase change (i.e., melting) before it reaches 337.3, (it doesn't) so
q = mcdT
To calculate the heat absorbed by the metal, we will use the formula:
Q = mcΔT
Where:
Q is the heat absorbed (in joules)
m is the mass of the metal (in kilograms)
c is the specific heat capacity of copper (in joules per kilogram per degree Celsius)
ΔT is the change in temperature (in degrees Celsius)
Let's break down the calculation step by step:
Step 1: Calculate the mass of the metal.
Given: Mass of copper metal = 77.40 kg
Step 2: Calculate the change in temperature.
Given: Initial temperature (Ti) = 19.6°C
Final temperature (Tf) = 337.3°C
ΔT = Tf - Ti = 337.3°C - 19.6°C = 317.7°C
Step 3: Determine the specific heat capacity of copper.
The specific heat capacity of copper is 0.385 J/g°C, which is equivalent to 385 J/kg°C.
Step 4: Convert the mass of the metal to grams.
Mass in grams = Mass in kilograms × 1000 = 77.40 kg × 1000 = 77,400 g
Step 5: Calculate the heat absorbed (Q) in joules.
Q = mcΔT
Q = (mass of the metal) × (specific heat capacity of copper) × ΔT
Q = 77,400 g × 385 J/kg°C × 317.7°C
Step 6: Convert the heat absorbed from joules to kilojoules.
Heat absorbed (in kJ) = Q ÷ 1000
Now, let's calculate the heat absorbed by the metal:
Q = 77,400 g × 385 J/kg°C × 317.7°C
Q ≈ 9,499,268,200 J
Heat absorbed (in kJ) = 9,499,268,200 J ÷ 1000
Heat absorbed ≈ 9,499,268 kJ
Therefore, the heat absorbed by the metal is approximately 9,499,268 kJ.