Two metal wires of identical dimensions are connected in series. If $\sigma$₁ and $\sigma$₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

1. $\frac{{\displaystyle 2{\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

2. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle 2{\sigma }_1{\sigma }_2}}$ 

3. $\frac{{\displaystyle {\sigma }_1+{\sigma }_2}}{{\displaystyle {\sigma }_1{\sigma }_2}}$  

4. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

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)

(a) 24 g                       

(b) 31.5g

(c) 42.5 g                   

(d) 22.5 g

A certain quantity of water cools from \(70^{\circ}\mathrm{C}\) to \(60^{\circ}\mathrm{C}\) in the first 5 minutes and to \(54^{\circ}\mathrm{C}\) in the next 5 minutes. 
The temperature of the surroundings will be: 

A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

(1) Stefan's law

(2) Wien's displacement law

(3) Kirchoff's law

(4) Newton's law of cooling

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?

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