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 black body is at a temperature of 5760 K. The energy of radiation emitted by the body at a wavelength of 250 nm is U₁, at a wavelength of 500 nm is U₂ and that at 1000 nm is U₃. Given Wien's constant $b=2.88\times {10}^6$ $nm-\mathrm{K,\; which }$of the following is correct?
1. U₃=0       
2. U₁>U₂
3. U₂>U₁     
4. U₁=0

The two ends of a metal rod are maintained at temperatures \(100^{\circ}\mathrm{C}\) and \(110^{\circ}\mathrm{C}\). The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures \(200^{\circ}\mathrm{C}\) and \(210^{\circ}\mathrm{C}\), the rate of heat flow will be:
1. 44.0 J/s
2. 16.8 J/s
3. 8.0 J/s
4. 4.0 J/s

The value of coefficient of volume expansion of glycerin is 5x10^-4 K^-1. The fractional change in the density of glycerin for a rise of 40°C in its temperature is -

1. 0.015
 

2. 0.020
 

3. 0.025
 

4. 0.010

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

1. 24 g                       

2. 31.5g

3. 42.5 g                   

4. 22.5 g

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

1.$\mathrm{ Q}/4{\mathrm{\pi R}}^2\mathrm{\sigma }$

2.${\left(\mathrm{ Q}/4{\mathrm{\pi R}}^2\mathrm{\sigma }\right)}^{-1/2}$

3.${\left(\mathrm{ 4}{\mathrm{\pi R}}^2\mathrm{Q}/\mathrm{\sigma }\right)}^{1/4}$

4.${\left(\mathrm{ Q}/4{\mathrm{\pi R}}^2\mathrm{\sigma }\right)}^{1/4}$

       $\left(\sigma s\tan ds for Stefan\text{'}s cons\tan t.\right)$

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. 

When 1 kg of ice at $0°\mathrm{C}$ melts to water at $0°\mathrm{C}$, the resulting change in its entropy, taking latent heat of ice to be $80 \mathrm{cal}/\mathrm{g},$ is

1.  $8\times {10}^4 \mathrm{cal}/\mathrm{K}$                                     

2.  $80 \mathrm{cal}/\mathrm{K}$

3.  $293 \mathrm{cal}/\mathrm{K}$                                         

4.  $273 \mathrm{cal}/\mathrm{K}$

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reserviors in time t ?

(1)Q/4                                         

(2)Q/16

(3)2Q                                           

(4)Q/2

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39°W$ and $239°W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39°C$ on the Celsius scale?

1. $78°W$                                   

2. $117°W$

3. $200°W$                                 

4. $139°W$