The formula to calculate the heat needed for a temperature change is:
\[\nQ = m \times c \times \Delta T\n\]
where:
- \( m \) represents the mass.
- \( c \) is the specific heat capacity.
- \( \Delta T \) is the temperature change.
For copper:
\[\nQ_{\text{copper}} = 6 \times 0.09 \times (20 - 10) = 6 \times 0.09 \times 10 = 5.4 \, \text{calories}\n\]
For lead:
\[\nQ_{\text{lead}} = 3 \times c_{\text{lead}} \times (100 - 20) = 3 \times c_{\text{lead}} \times 80\n\]
Given the heat required for copper equals the heat needed for lead:
\[\n5.4 = 3 \times c_{\text{lead}} \times 80\n\]
Solving for \( c_{\text{lead}} \):
\[\nc_{\text{lead}} = \frac{5.4}{3 \times 80} = \frac{5.4}{240} = 0.0225 \, \text{cal/g}^\circ C\n\]
Therefore, the specific heat of lead is approximately \( 0.022 \, \text{cal/g}^\circ C \).