The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:
1. \(-40^\circ\)
2. \(40^\circ\)
3. \(0^\circ\)
4. \(50^\circ\)

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

The triple points of neon and carbon dioxide are \(24.57\) K and \(216.55\) K respectively. The value of these temperatures on Fahrenheit scales will be: 

The ice-point reading on a thermometer scale is found to be \(20^\circ,\) while the steam point is found to be \(70^\circ.\) When this thermometer reads \(100^\circ ,\) the actual temperature is:
1. \(80^\circ~\mathrm{C}\)
2. \(130^\circ~\mathrm{C}\)
3. \(160^\circ~\mathrm{C}\)
4. \(200^\circ~\mathrm{C}\)

The coefficient of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\). Lengths of brass and steel rods are \(L_1\) and \(L_2\) respectively. If \((L_2-L_1)\) remains the same at all temperatures, which one of the following relations holds good?
1. \(\alpha_1L_2^2=\alpha_2L_1^2\)
2. \(\alpha_1^2L_2=\alpha_2^2L_1\)
3. \(\alpha_1L_1=\alpha_2L_2\)
4. \(\alpha_1L_2=\alpha_2L_1\)

The coefficient of area expansion \(\beta\) of a rectangular sheet of a solid in terms of the coefficient of linear expansion \(\alpha\) is:
1. \(2\alpha\)
2. \(\alpha\)
3. \(3\alpha\)
4. \(\alpha^2\)

A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:
1. \(\alpha_A\)
2. \(\frac{2\alpha_A}{6}\)
3. \(\frac{4\alpha_A}{6}\)
4. \(\frac{5\alpha_A}{6}\)

A brass wire \(1.8\) m long at \(27\) °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of\(-39\) °C, what is the tension created in a wire with a diameter of \(2.0\) mm? (coefficient of linear expansion of brass \(=2.0 \times10^{-5}\) K^-1, Young's modulus of brass\(=0.91 \times10^{11}\) Pa)
1. \(3.8 \times 10^3\) N
2. \(3.8 \times 10^2\) N
3. \(2.9 \times 10^{-2}\) N
4. \(2.9 \times 10^{2}\) N