An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are 24 times 10^-6/^circmathrmC$24 \times 10^{-6}/^{\circ}\mathrm{C}$ and 1.2 times 10^-5/^circmathrmC$1.2 \times 10^{-5}/^{\circ}\mathrm{C}$, respectively. The length of this composite rod when its temperature is raised to 100°C, is ____ cm.

### Related Formula Delta l = l_0 alpha Delta T$$\Delta l = l_0 \alpha \Delta T$$ l_textfinal = l_1 + l_2 + Delta l_1 + Delta l_2$$l_{\text{final}} = l_1 + l_2 + \Delta l_1 + \Delta l_2$$ ### Core Logic Let the original lengths be l_0A$l_{0A}$ (aluminium) and l_0S$l_{0S}$ (steel). They have same length, so l_0A = l_0S = 60text cm$l_{0A} = l_{0S} = 60\text{ cm}$. Change in temperature Delta T = 100^circtextC - 30^circtextC = 70^circtextC$\Delta T = 100^{\circ}\text{C} - 30^{\circ}\text{C} = 70^{\circ}\text{C}$. Expansion of Aluminium: Delta l_A = l_0 alpha_A Delta T$\Delta l_A = l_0 \alpha_A \Delta T$ Expansion of Steel: Delta l_S = l_0 alpha_S Delta T$\Delta l_S = l_0 \alpha_S \Delta T$ ### Step 1: Calculate Final Length l_textfinal = l_0(1 + alpha_A Delta T) + l_0(1 + alpha_S Delta T)$$l_{\text{final}} = l_0(1 + \alpha_A \Delta T) + l_0(1 + \alpha_S \Delta T)$$ l_textfinal = l_0 [2 + (alpha_A + alpha_S)Delta T]$$l_{\text{final}} = l_0 [2 + (\alpha_A + \alpha_S)\Delta T]$$ l_textfinal = 60 left[ 2 + (24 times 10^-6 + 12 times 10^-6) times 70 right]$$l_{\text{final}} = 60 \left[ 2 + (24 \times 10^{-6} + 12 \times 10^{-6}) \times 70 \right]$$ l_textfinal = 60 left[ 2 + (36 times 10^-6) times 70 right]$$l_{\text{final}} = 60 \left[ 2 + (36 \times 10^{-6}) \times 70 \right]$$ l_textfinal = 60 [2 + 0.00252] = 120 + 60(0.00252) = 120 + 0.1512 = 120.15text cm$$l_{\text{final}} = 60 [2 + 0.00252] = 120 + 60(0.00252) = 120 + 0.1512 = 120.15\text{ cm}$$

### Pattern Recognition For composite rods connected end-to-end, expansions simply add up. Convert 1.2 times 10^-5$1.2 \times 10^{-5}$ to 12 times 10^-6$12 \times 10^{-6}$ immediately for easy mental addition. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Thermal Properties of Matter