Conduction Law

Q.

Consider a compound slab consisting of two different materials having equal lengths, thicknesses and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is

1. $\sqrt{2}K$

2. $3K$

3. $\frac{4}{3}K$

4. $\frac{2}{3}K$

Q.

The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio

1. 4 : 5

2. 9 : 1

3. 1 : 9

4. 5 : 4

Q. 22. An iron bar of (K is 79W mK )and a brass bar (K is 109W mk) both of equal length and area of 0.1m and 0.02m2 respectively are soldered end to end. The free ends of iron bar and brass bar are at 373 k and 273k respectively. Obtain equivalent thermal conductivity of the compound bar.

Q. Two identical square rods of metal are welded end to end as shown in figure $\left(a\right)$, $20\text{calories}$ of heat flows through it in $4\text{minutes}$. If the rods are welded as shown in figure $\left(b\right)$, the same amount of heat will flow through the rods in

1. $1\text{minute}$
2. $2\text{minutes}$
3. $4\text{minutes}$
4. $16\text{minutes}$

Q. 20. The specific heat of silver is 0.0565cal/g^° C. Assuming no loss of heat to the surrounding or system, calculate the final temperature when 100g of silver at 40^° C is immersed in 60g of water at 10^° C.

Q.

The length of mercury thread in a thermometer at 100° C and 50°C is 10 cm and 4 cm, respectively. What is the length of the mercury thread when it is kept in contact with melting ice?

1. 0

2. 2 cm

3. 1 cm

4. 3 cm

Q. Consider two hot bodies $B_{1}and{B}_2$ which have temperatures ${100}^{o}Cand{80}^{o}C$ respectively at t=0. The temperature of the surroundings is ${40}^{o}C$. The ratio of the respective rates of cooling $R_{1}and{R}_2$ of these two bodies at t=0 will be

1. 

2. 

3. 

4. 

Q.

1. Calculate the relation between coefficient of volume expansion and coefficient of linear expansion.

Q.

Find the equivalent thermal conductivity of the given rod.

1. $\frac{2K}{3}$

2. $3K$

3. $\frac{3K}{2}$

4. $\frac{4K}{3}$

Q. Two thin concentric shells made of copper with radius r1 & r2 (r2>r1) have material of thermal conductivity k filled between them. The inner & outer spheres are maintained at T1 & T2 respectively by keeping a heater of power P at the center of two spheres. Find the value of P.

Q. 16.A wall has 2 layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity for A is twice that of British and, under steady condition, the temperature difference across the wall is 36 degree Celsius. The temperature difference across the layer A is.

Q. Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities K and 2K in series. The equivalent conductivity of the slab is.

Q. A solid iron sphere of density ρ, emissivity e, and specific heat C has radius R. If it is heated to temperature 400 K and suspended inside a chamber whose walls are almost 0 K, then what is the time required for the temperature of the sphere to drop to 200 K?

Q. A body cools in $7$ min from ${60}^{\circ }\text{C}$ to ${40}^{\circ }\text{C}$. What will be its temperature after the next $7$ min ?
The temperature of surroundings is ${10}^{\circ }\text{C}$. [Assume Newton's Law of cooling is applicable]

1. $T={32}^{\circ }\text{C}$
2. $T={28}^{\circ }\text{C}$
3. $T={24}^{\circ }\text{C}$
4. $T={36}^{\circ }\text{C}$

Q. Which of the following factors affect the thermal conductivity of a rod?

1. Area of cross-section
2. Length of rod
3. Material of rod
4. All of these

Q. a slab consists of two parellel layers of two different materials of same thickness having thermal conductivities of K1 and K2 . show that the equivalent conductivities of the combination is( K1+K2)/2

Q. the rate of change of magnetic flux density through a circular coil of area 10 race to-2msquare and number of turns 100 is 10 race to 3 wb/msquare sec.the value of induced emf will be?

Q. A ‘thermacole’ icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of 5.0 cm. If 4.0 kg of ice is put in the box, estimate the amount of ice remaining after 6 h. The outside temperature is 45 °C, and co-efficient of thermal conductivity of thermacole is 0.0 s¯¹m–1 K¯¹. [Heat of fusion of water = 335 × 103 J kg¯¹]

Q. Two walls of thickness $d_1$ and $d_2$, thermal conductivities $K_1$ and $K_2$ are in contact. In the steady state, if the temperature at the outer surfaces are $T_1$ and $T_2$, the temperature at the contact of the walls will be

1. $\frac{K_1{T}_1+K_2{T}_2}{d_1+d_2}$
2. $\frac{K_1{T}_1{d}_2+K_2{T}_2{d}_1}{K_1{d}_2+K_2{d}_1}$
3. $\frac{(K_1{d}_1+K_2{d}_2)T_1{T}_2}{T_1+T_2}$
4. $\frac{K_1{d}_1{T}_1+K_2{d}_2{T}_2}{K_1{d}_1+K_2{d}_2}$

Q. One end of a copper rod of uniform cross section and length $1.5\text{m}$ is in contact with ice and the other end with steam at ${100}^{\circ }\text{C}$. At what point along its length from $\text{A}$ should a temperature of ${200}^{\circ }\text{C}$ be maintained so that in steady state, the mass of the ice melting is equal to that of steam produced in the same interval of time . $[L_v=540\text{cal/g},L_f=80\text{cal/ g}]$

1. $10.34\text{cm}$
2. $9.1\text{cm}$
3. $20\text{cm}$
4. $5\text{cm}$

Q. The two opposite faces of a cubical piece of iron (thermal conductivity = 0.2 CGS units) are at 100 °C and 0 °C in ice. If the area of a surface is 4 cm2, then the mass of ice melted in 10 minutes will be

Q. The net thermal resistance of two identical rods connected in parallel is less than that of resistance offered by each rod individually.

1. False
2. True

Q.

A rod CD of thermal resistance 5.0 K/W is joined at the middle of an identical rod AB as shown in figure The ends A, B and D are maintained at 100${}^{\circ }$C, 0 ${}^{\circ }$ C and 25 ${}^{\circ }$ C respectively. Find the heat current in CD.

1. 2W

2. 8W

3. 4W

4. 6W

Q. Which of the following options is incorrect in reference to Fourier's law of heat conduction?

1. Rate of heat flow is proportional to the cross-sectional area of rod
2. Rate of heat flow is proportional is the temperature difference between the ends of the rod
3. Rate of heat flow is inversely proportional to thickness of the rod
4. Rate of heat flow is proportional to the coefficient of thermal conductivity of material of the rod

Q. A copper block and a wooden block having similar dimensions are subjected to the same temperature at one face of each block. The other face of the blocks will reach the same temperture at a rate which is:

1. Faster in wooden block.
2. Faster in copper block.
3. Equal in wooden as well as copper block.
4. Cannot be predicted with given data.

Q.

Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is

1. 2 :

2. 3 : 2

3. 1 : 2

4. p : 2

Q. Explain why :
(a) A body with large reflectivity is a poor emitter
(b) A brass tumbler feels much colder than a wooden tray on a chilly day
(c) An optical pyrometer (for measuring high temperatures ) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace
(d) The earth without its atmosphere would be inhospitably cold
(e) Heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

Q. Which of the following options is incorrect in reference to Fourier's law of heat conduction?

1. Rate of heat flow is proportional to the cross-sectional area of rod
2. Rate of heat flow is proportional is the temperature difference between the ends of the rod
3. Rate of heat flow is inversely proportional to thickness of the rod
4. Rate of heat flow is proportional to the coefficient of thermal conductivity of material of the rod

Q. Two particles $A$ and $B$ are moving on two concentric circles of radii $R_1\text{and}{R}_2$ with equal angular speed $\omega$. At $t=0$, their positions and direction of motion are shown in the figure :


The relative velocity $\overrightarrow{v_A}-\overrightarrow{v_B}\text{at}t=\frac{\pi }{2\omega }$ is given by :

1. $\omega (R_1-R_2)\hat{i}$
2. $\omega (R_1+R_2)\hat{i}$
3. $-\omega (R_1+R_2)\hat{i}$
4. $\omega (R_2-R_1)\hat{i}$

Q. The coefficient of thermal conductivity of copper, mercury and glass are respectively $K_C,K_m$ and $K_g$ such that $K_c>K_m>K_g$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_C,X_m$ and $X_g$, then

1. $X_c=X_m=X_g$
2. $X_c>X_m>X_g$
3. $X_c<X_m<X_g$
4. $X_m<X_c<X_g$