Respuesta :
[tex] Q = 10.4 \; \text{kJ} [/tex]
The specific heat of a material gives the energy it takes to increase the temperature of one unit mass of the material by one unit temperature. The SI unit for specific heat [tex] c [/tex] is therefore [tex] \text{J} /\text{kg} \cdot \textdegree{\text{C}} [/tex].
The formula relating the energy required to raise the temperature of [tex] m [/tex] grams of a substance with specific energy [tex] c [/tex] by [tex] \Delta T [/tex] degrees is
[tex] Q= c \cdot m \cdot \Delta T [/tex]
The question provides the following information:
- [tex] c = 130\; \text{J} /\text{kg} \cdot \textdegree{\text{C}} [/tex] for gold
- [tex] m= 1 \; \text{kg} [/tex]
- [tex] \Delta T = 100 \textdegree{\text{C}} - 20 \textdegree{\text{C}} = 80 \textdegree{\text{C}} [/tex]
Apply the formula:
[tex] \begin{array}{ccc}
Q & = & c \cdot m \cdot \Delta T\\
& = & 130 \; \text{J} \cdot \text{kg}^{-1} \cdot \textdegree{\text{C}}^{-1} \times 1 \; \text{kg} \times 80 \; \textdegree{\text{C}}\\
& = & 1.04 \times 10^{4} \;\text{J}\\
& = & 10.4 \; \text {kJ} \end{array} [/tex]
[tex] [/tex]