On a new scale of temperature (which is linear) and called the \(\text W\) scale, the freezing and boiling points of water are \(39^{\circ}\text{ W}\) and   \(239^{\circ}\text{ W}\)$\mathrm{}$ respectively. What will be the temperature on the new scale, corresponding to a temperature of\(39^{\circ}\text{C}\) on the Celsius scale?
1. \(78^{\circ}\text{ W}\)
2. \(117^{\circ}\text{ W}\)
3. \(200^{\circ}\text{ W}\)
4. \(139^{\circ}\text{ W}\)$$

A copper rod of \(88\) cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is: 
\((\alpha_{Cu}=1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}=2.2\times10^{-5}~\text{K}^{-1})\)
1. \(68\) cm

2. \(6.8\) cm

3. \(113.9\) cm

4. \(88\) cm

Two different wires having lengths \(L_1\) and \(L_2, \) and respective temperature coefficient of linear expansion \(\alpha_1\) and \(\alpha _2, \) are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

1. \( 4 \dfrac{\alpha_1 \alpha_2}{\alpha_1+\alpha_2} \dfrac{L_2 L_1}{\left(L_2+L_1\right)^2} \)

2. \( 2 \sqrt{\alpha_1 \alpha_2} \)

3. \( \dfrac{\alpha_1+\alpha_2}{2} \)

4. \( \dfrac{\alpha_1 L_1+\alpha_2 L_2}{L_1+L_2}\)