To determine the thermal capacity of \(5 \, \text{kg}\) of copper, we can use the formula for thermal capacity, which is given by:
[tex]\[ C = m \times s \][/tex]
where:
- \(C\) is the thermal capacity,
- \(m\) is the mass of the substance,
- \(s\) is the specific heat capacity of the substance.
For this particular problem:
- The mass of copper, \(m\), is \(5 \, \text{kg}\),
- The specific heat capacity of copper, \(s\), is \(380 \, \text{Jkg}^{-1}{}^{\circ}\text{C}^{-1}\).
Using the formula, we substitute the given values:
[tex]\[ C = 5 \, \text{kg} \times 380 \, \text{Jkg}^{-1}{}^{\circ}\text{C}^{-1} \][/tex]
Now, we carry out the multiplication:
[tex]\[ C = 5 \times 380 \][/tex]
[tex]\[ C = 1900 \, \text{J}{}^{\circ}\text{C}^{-1} \][/tex]
Hence, the thermal capacity of \(5 \, \text{kg}\) of copper is \(1900 \, \text{J}{}^{\circ}\text{C}^{-1}\).
To express this in scientific notation:
[tex]\[ 1900 = 1.9 \times 10^3 \][/tex]
Therefore, the thermal capacity of [tex]\(5 \, \text{kg}\)[/tex] of copper is [tex]\(1.9 \times 10^3 \, \text{J}{}^{\circ}\text{C}^{-1}\)[/tex].
