To analyze the temperature changes in the two pieces of metal based on the specific heat formula, we can use the following equation for heat transfer:
\[ q = mc\Delta T \]
Where:
- \(q\) is the heat energy absorbed or released (in joules),
- \(m\) is the mass (in grams),
- \(c\) is the specific heat capacity (in J/g-K), and
- \(\Delta T\) is the change in temperature (in K or °C, since the scale is the same).
Let's denote the specific heat of the first block as \(c_1\) and the specific heat of the second block as \(c_2\).
For the first block, we have:
\[ q_1 = m \cdot c_1 \cdot (3°C) \]
For the second block, we have:
\[ q_2 = m \cdot c_2 \cdot (8°C) \]
Since both blocks are made of the same mass and are absorbing energy from the same source (the sunlight), we can assume that the heat gained, \(q\), must be equal for both blocks, hence:
\[ q_1 = q_2 \]
Substituting the expressions for \(q_1\) and \(q_2\):
\[ m \cdot c_1 \cdot (3) = m \cdot c_2 \cdot (8) \]
Here, \(m\) cancels out from both sides (since they are equal):
\[ c_1 \cdot (3) = c_2 \cdot (8) \]
Now we can solve for \(c_1\):
\[ c_1 = \frac{c_2 \cdot (8)}{3} \]
Substituting \(c_2 = 0.24 , \text{J/g-K}\):
\[ c_1 = \frac{0.24 \cdot 8}{3} \]
Calculating \(c_1\):
\[ c_1 = \frac{1.92}{3} = 0.64 , \text{J/g-K} \]
Therefore, the specific heat of the first block is:
B. 0.64 J/g-K.