If the energy used to heat up a block of 2kg of copper is 115.8 kJ, what is the temperature it was heated to if the starting temperature was 100oC and the specific heat capacity is 386 J/kgK.
To find the final temperature that the block of copper was heated to, we can use the equation:
Q = m * c * ΔT
Where:
Q is the energy transferred (in joules),
m is the mass of the object (in kilograms),
c is the specific heat capacity of the material (in joules per kilogram per degree Celsius),
ΔT is the change in temperature (in degrees Celsius).
In this case, we are given:
Q = 115.8 kJ = 115.8 * 1000 J (converting kilojoules to joules)
m = 2 kg
c = 386 J/kgK (specific heat capacity of copper)
Initial temperature, Ti = 100 °C
We need to rearrange the equation to solve for ΔT:
ΔT = Q / (m * c)
Plugging in the given values:
ΔT = 115.8 * 1000 J / (2 kg * 386 J/kgK)
Simplifying the equation:
ΔT = 115800 J / (772 J/K)
ΔT ≈ 150.26 K
To find the final temperature, Tf, we add this change in temperature to the initial temperature:
Tf = Ti + ΔT
Tf = 100 °C + 150.26 K
Note that Celsius and Kelvin have the same scale, so we can directly add them:
Tf ≈ 250.26 °C
Therefore, the block of copper was heated to approximately 250.26 °C.