A deep rectangular pond of surface area \(A\), containing water (density = \(\rho,\) specific heat capacity = \(s\)), is located in a region where the outside air temperature is at a steady value of \(-26^{\circ}\text{C}\)$$. The thickness of the ice layer in this pond at a certain instant is \(x\). Taking the thermal conductivity of ice as \(k\), and its specific latent heat of fusion as \(L\), the rate of increase of the thickness of the ice layer, at this instant, would be given by:
1. \(\dfrac{26k}{x\rho L-4s}\)
2. \(\dfrac{26k}{x^2\rho L}\)
3. \(\dfrac{26k}{x\rho L}\)
4. \(\dfrac{26k}{x\rho L+4s}\)

Two uniform rods of length \(L\) and \(2L\) and thermal coefficient of linear expansion \(2\alpha\)  and \(\alpha\) respectively, are connected as shown in the figure. The equivalent coefficient of linear expansion is:

                 
1. \(\frac{3\alpha}{4}\)
2. \(\frac{4\alpha}{3}\)
3. \(\frac{2\alpha}{3}\)
4. \(\frac{5\alpha}{3}\)

An object kept in a large room having an air temperature of \(25^\circ \text{C}\) takes \(12\) minutes to cool from \(80^\circ \text{C}\) to \(70^\circ \text{C}.\) The time taken to cool for the same object from \(70^\circ \text{C}\) to \(60^\circ \text{C}\) would be nearly:
1. \(10\) min
2. \(12\) min
3. \(20\) min
4. \(15\) min

Which of the following statement is correct regarding heat transfer?

1.  Forced convection requires gravity

2.  Natural convection requires gravity

3.  Radiation and forced convection requires gravity

4.  Neither natural nor forced convection requires gravity

The fundamental interval, that is the number of division between LFP & UFP on the two scales X and Y are 50 and 150 respectively. The ice point on both the scales is  $0°$. If the temperature on the X-scale is $15°$, then what is the temperature on the Y-scale ?

$1. 30°$
$2. 45°$
$3. 60°$
$4. 75°$

Recently, the phenomenon of super conductivity has been observed at 73 K. This temperature is nearly equal to

1. $-288°\mathrm{F}$

2. $-146°\mathrm{F}$

3. $-328°\mathrm{F}$

4. $+178°\mathrm{F}$

If a graph is plotted between the temperature of a body in degrees Celsius (along the \(\mathrm{y}\)-axis) and Fahrenheit (along the \(\mathrm{x}\)-axis) at different temperatures, then the slope of the graph will be:
1. \(\frac{5}{9}\)

2. \(\frac{9}{5}\)

3. \(\frac{3}{5}\)

4. \(\frac{5}{3}\)

Which of the following is true in modern thermometry?

1. Triple point of water is fixed

2. Boiling point of water is fixed

3. Melting point of ice is fixed

4. Dew point is fixed

A metal wire of length l and area of cross-section A is fixed at its ends by rigid supports at negligible tension. If this wire is cooled, then the tension in it will be

1. Proportional to l

2. Inversely proportional to l

3. Independent of l

4. Independent of A

Which temperature on the Fahrenheit scale is numerically the same as that on the Celsius scale?

1. $-40°\mathrm{F}$

2. $-42°\mathrm{F}$

3. $-70°\mathrm{F}$

4. $-72°\mathrm{F}$