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 temperature of a body on the Kelvin scale is found to be \(x^\circ~\text K.\) When it is measured by a Fahrenheit thermometer, it is found to be \(x^\circ~\text F,\) then the value of \(x\) is:
1. \(40\)
2. \(313\)
3. \(574.25\)
4. \(301.25\)

The value of the coefficient of volume expansion of glycerin is \(5\times10^{-4}\) K^-1. The fractional change in the density of glycerin for a temperature increase of \(40^\circ \mathrm{C}\) will be:

The coefficients 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 (\(l_2-l_1\)) is maintained the same at all temperatures, Which one of the following relations holds good?
1. \(\alpha_1 l_2^2=\alpha_2l_1^2\)
2. \(\alpha_1^2 l_2=\alpha_2^2l_1\)
3. \(\alpha_1 l_1=\alpha_2l_2\)
4. \(\alpha_1 l_2=\alpha_2l_1\)

A copper rod of \(88\) cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is:
\(\left(\alpha_{Cu}= 1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}= 2.2\times10^{-5}~\text{K}^{-1}\right)\)
1. \(68~\text{cm}\)
2. \(6.8~\text{cm}\)
3. \(113.9~\text{cm}\)
4. \(88~\text{cm}\)

A pendulum clock runs faster by \(5\) s per day at \(20^{\circ}\mathrm {C}\) and goes slow by \(10\) s per day at \(35^{\circ}\mathrm {C}\). It shows the correct time at a temperature of:
1. \(27.5^{\circ}\mathrm {C}\)
2. \(25^{\circ}\mathrm {C}\)
3. \(30^{\circ}\mathrm {C}\)
4. \(33^{\circ}\mathrm {C}\)

Two rods, one made of aluminium and the other made of steel, having initial lengths \(l_1\) and \(l_2\) are connected together to form a single rod of length $l_1+l_2$. The coefficient of linear expansion for aluminium and steel are ${\alpha }_a$ and ${\alpha }_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by \(t^\circ \mathrm{C},\) then the ratio \(\frac{l_1}{l_1+l_2}\) is:
1. $\frac{{\alpha }_s}{{\alpha }_a}$

2. $\frac{{\alpha }_a}{{\alpha }_s}$

3. $\frac{{\alpha }_a}{{\alpha }_a+{\alpha }_s}$

4. $\frac{{\alpha }_s}{{\alpha }_a+{\alpha }_s}$

The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.

What will be switched on when the bimetallic strip becomes hot?

A metal bar of length \(L\) and area of cross-section \(A\) is clamped between two rigid supports. For the material of the rod, it's Young’s modulus is \(Y\) and the coefficient of linear expansion is \(\alpha.\) If the temperature of the rod is increased by \(\Delta t^{\circ} \text{C},\) the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)