A slab of stone of area of 0.36 ${\mathrm{m}}^2$ and 

thickness 0.1 m is exposed on the lower 

surface to steam at $100°\mathrm{C}$. A block of ice 

at $0°\mathrm{C}$ rests on the upper surface of the slab.

In one hour 4.8 kg of ice is melted. The thermal

conductivity of slab is

(Given latent heat of fusion of ice 

=3.36x${10}^{5 }\mathrm{J} {\mathrm{kg}}^{-1}$)

(a) $1.24 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$        (b) $1.29 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$

(c) $2.05 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$        (d) $1.02 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$

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 thermocouple of negligible resistance produces an emf of $40 \mathrm{\mu V}/°\mathrm{C}$ in the linear range of temperature. A galvanometer of resistance $10 \mathrm{\Omega }$ whose sensitivity is $1 \mathrm{\mu A}/\mathrm{div},$ is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be

(a) $0.5°\mathrm{C}$                                       (b) $1°\mathrm{C}$

(c) $0.1°\mathrm{C}$                                       (d) $0.25°\mathrm{C}$

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

The total radiant energy per unit area per unit time, normal to the direction of incidence, received at a distance R from the centre of a star of radius r,whose outer surface radiates as a black body at a temperature TK is given by 

(a) $\sigma r^2{T}^4/R^2$                                       (b) $\sigma r^2{T}^4/4{\mathrm{\pi r}}^2$

(c) $\sigma r^4{T}^4/r^4$                                        (d) $4\mathrm{\pi } \sigma r^2{T}^4/R^2$

(where $\sigma$ is Stefan's constant)

A black body at $227°C$ radiates heat at the rate of 7 cal $c{m}^{-2}{s}^{-1}.$ At a temperature of $727°C,$ the rate of heat radiated in the same units will be 

(1) 60                                     

(2) 50

(3) 112                                   

(4) 80

The two ends of a rod of length L and a uniform cross-sectional area A are kept at two temperatures $T_1 and T_2\left(T_1> T_2\right).$The rate f heat transfer, $\frac{dQ}{dt},$ through the rod in a steady state is given by 

(1) $\frac{dQ}{dt}=\frac{KL\left(T_1-T_2\right)}{A}$                       

(2) $\frac{{\displaystyle dQ}}{{\displaystyle dt}}=\frac{{\displaystyle KL\left(T_1-T_2\right)}}{{\displaystyle LA}}$

(3) $\frac{dQ}{dt}=KLA\left(T_1-T_2\right)$                     

(4) $\frac{dQ}{dt}=\frac{KA\left(T_1-T_2\right)}{L}$

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) $139°W$

To keep constant time, watches are fitted with balance wheel made of -

(1) Invar                                 

(2) Stainless steel

(3) Tungsten                             

(4) Platinum

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. \(Y\alpha AL\Delta t\)