Question

How much energy must be added to a 1 kg piece of gold with a specific heat of 130 j/kg to increase its temperature from 20 c to 100c?

Answer 1

$Q = 10.4 \; \text{kJ}$

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 $c$ is therefore $\text{J} /\text{kg} \cdot \textdegree{\text{C}}$.

The formula relating the energy required to raise the temperature of $m$ grams of a substance with specific energy $c$ by $\Delta T$ degrees is

$Q= c \cdot m \cdot \Delta T$

The question provides the following information:

• $c = 130\; \text{J} /\text{kg} \cdot \textdegree{\text{C}}$ for gold
• $m= 1 \; \text{kg}$
• $\Delta T = 100 \textdegree{\text{C}} - 20 \textdegree{\text{C}} = 80 \textdegree{\text{C}}$

Apply the formula:

$\begin{array}{ccc} Q & = & c \cdot m \cdot \Delta T\\ & = & 130 \; \text{J} \cdot \text{kg}^{-1} \cdot \textdegree{\text{C}}^{-1} \times 1 \; \text{kg} \times 80 \; \textdegree{\text{C}}\\ & = & 1.04 \times 10^{4} \;\text{J}\\ & = & 10.4 \; \text {kJ} \end{array}$