$\mathrm{If}<mspace\; width="1em"></mspace>{\mathrm{\alpha }}_{\mathrm{c}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{\alpha }}_{\mathrm{f}}<mspace\; width="1em"></mspace>\mathrm{denote}<mspace\; width="1em"></mspace>\mathrm{the}<mspace\; width="1em"></mspace>\mathrm{numerical}<mspace\; width="1em"></mspace>\mathrm{values}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{coefficient}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{linear}<mspace\; width="1em"></mspace>$
$\mathrm{expansion}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\mathrm{solid},<mspace\; width="1em"></mspace>\mathrm{expressed}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>\mathrm{per}<mspace\; width="1em"></mspace>°\mathrm{C}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{per}<mspace\; width="1em"></mspace>°\mathrm{F}<mspace\; width="1em"></mspace>\mathrm{respectively},$
$<mspace\; width="1em"></mspace>\mathrm{then}$

1.  ${\alpha }_c<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\alpha }_f<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

2.  ${\alpha }_f<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\alpha }_c<mspace\; width="1em"></mspace>$

3.  ${\alpha }_f<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\alpha }_c<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.  ${\alpha }_f<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\alpha }_c<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>0$

$$\begin{gathered} \mathrm{A}<mspace\; width="1em"></mspace>\mathrm{pendulum}<mspace\; width="1em"></mspace>\mathrm{clock}<mspace\; width="1em"></mspace>\mathrm{runs}<mspace\; width="1em"></mspace>\mathrm{fast}<mspace\; width="1em"></mspace>\mathrm{by}<mspace\; width="1em"></mspace>5<mspace\; width="1em"></mspace>\sec .<mspace\; width="1em"></mspace>\mathrm{per}<mspace\; width="1em"></mspace>\mathrm{day}<mspace\; width="1em"></mspace>\mathrm{at}<mspace\; width="1em"></mspace>20°\mathrm{C}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{goes}<mspace\; width="1em"></mspace>\mathrm{slow} \\ <mspace\; width="1em"></mspace>\mathrm{by}<mspace\; width="1em"></mspace>10<mspace\; width="1em"></mspace>\sec .<mspace\; width="1em"></mspace>\mathrm{per}<mspace\; width="1em"></mspace>\mathrm{day}<mspace\; width="1em"></mspace>\mathrm{at}<mspace\; width="1em"></mspace>35°\mathrm{C}.<mspace\; width="1em"></mspace>\mathrm{It}<mspace\; width="1em"></mspace>\mathrm{shows}<mspace\; width="1em"></mspace>\mathrm{correct}<mspace\; width="1em"></mspace>\mathrm{time}<mspace\; width="1em"></mspace>\mathrm{at}<mspace\; width="1em"></mspace>\mathrm{a}<mspace\; width="1em"></mspace>\mathrm{temperature}<mspace\; width="1em"></mspace>\mathrm{of}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace> \end{gathered}$$

1.  $27.5°\mathrm{C}<mspace\; width="1em"></mspace>$

2.  $25°\mathrm{C}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

3.  $30°\mathrm{C}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$

4.  $33°\mathrm{C}$

Two identical bodies are made of a material whose heat capacity increases with temperature. One of these is at ${\mathrm{}}^{}$\(100^{\circ} \mathrm{C}\), while the other one is at ${\mathrm{}}^{}$\(0^{\circ} \mathrm{C}\). If the two bodies are brought into contact, then assuming no heat loss, the final common temperature will be:

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4x10⁵J/Kg and g=10N/Kg]

1. 544 km

2. 136 km

3.  68  km

4.  34 km

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:

Steam at \(100^{\circ}\mathrm{C}\) is injected into 20 g of \(10^{\circ}\mathrm{C}\) water. When water acquires a temperature of \(80^{\circ}\mathrm{C}\), the mass of water present will be: (Take specific heat of water =1 cal g^-1 \(^\circ\)C^-1 and latent heat of steam = 540 cal g^-1)

Liquid oxygen at 50K is heated to 300K at constant pressure of 1 atm. The rate of heating is constant.Which one of the following graphs represents the variation of temperature with time?

1. 

2. 

3. 

4. 

The coefficient of linear expansion of brass and steel are ${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_2$ at 0°C, their difference in length $\left(l_2-l_1\right)$ will remain the same at a temperature if

1. ${\alpha }_1{l}_2={\alpha }_2{l}_1$                                 

2. ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$

3. ${\alpha }_1^2{l}_1={\alpha }_2^2{l}_2$                                   

4. ${\alpha }_1{l}_1={\alpha }_2{l}_2$

Heat travels through vacuum by 

1. Conduction                 

2. Convection

3. Radiation                     

4. Both (1) and (2)

We consider the radiation emitted by the human body. Which of the following statements is true?

(1) The radiation is emitted only during the day.

(2) The radiation is emitted during the summers and absorbed during the winters.

(3) The radiation emitted lies in the ultraviolet region and hence is not visible.

(4) The radiation emitted is in the infra-red region.