Conduction Law

Q.

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of 0.1gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in gm/sec will be

1. 3.2
2. 1.6
3. 0.1
4. 0.2

Q. A partition wall has two layers A and B in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. If the steady state temperature difference across the wall is 60k, then the corresponding difference across the layer A is

1. 20 K
2. 30 K
3. 40 K
4. 10 K

Q.

Two different metal rods of the same length their ends kept at the same temperatures ${\theta }_1$ and ${\theta }_2$ with ${\theta }_2$ > ${\theta }_1$ If $A_1$ and $A_2$ are their cross-sectional area and $K_1$ and $K_2$ their thermal conductivities, the rate of flow of heat in the two rods will be the same if

1. 

2. 

3. 

4. 

Q. Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ }C$ and ${90}^{\circ }C$ respectively. The temperature of junction of the three rods will be

1. ${30}^{\circ }C$
2. ${45}^{\circ }C$
3. ${60}^{\circ }C$
4. ${20}^{\circ }C$

Q.

What is the SI unit of the coefficient of thermal conductivity?

1. 

2. 

3. 

4. 

Q. If the earth shrinks half in radius with its mass remaining the same, the weight of an object on earth will :

1. decrease by $50$%
2. increase by $300$%
3. increase by $50$%
4. decrease by $25$%

Q.

One end of a copper rod of length 1.0 m and area of cross-section ${10}^{-3}$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92cal/m-s{-}^{\circ }C$ and the latent heat of ice is $8\times {10}^{4}cal/kg$, then the amount of ice which will melt in one minute is

1. 
   
2. 
3. 
4. 

Q. A metallic rod of cross-sectional area $20c{m}^2$, with the lateral surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice water mixture. The heat conducted through the rod melts the ice at the rate of $1$ gm for every $84$ sec. The thermal conductivity of the rod is $160W{m}^1{K}^1$. Latent heat of $ice=80cal/gm,1cal=4.2joule$. What is the length (in m) of the rod?

1. $4m$
2. $5m$
3. $8m$
4. $10m$

Q. Electric field , in a straight solid uniform cylindrical conductor of radius R = 2 cm is along the axis of the cylinder and is given by E = K r where K = 1$\times {10}^8$ Volt/Metre${}^2$ and r is the distance (In metre) from the axis of the cylinder. If current in the cylinder is I = 16$\pi$ micro ampere. If the specific conductivity $\sigma =\frac{z}{5}\times {10}^{-8}{\Omega }^{-1}{m}^{-1}$, the value of Z is

1. 12
2. 15
3. 5
4. 10

Q. A cylindrical aluminium rod of length 2m is maintained at a temperature difference of 10${}^{\circ }$ Celsius. The radius of the rod is 1 cm. Will it make a difference if it were a steel rod of same dimensions?

1. Yes
2. No

Q. Two metal cubes A and B of same size are arranged as shown in figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A and B are 300 W/m ${}^{\circ }C$, and 200 W/m ${}^{\circ }C$, respectively. After steady state is reached the temperature T of the interface will be ….

1. $T={60}^{\circ }C$
2. $T={70}^{\circ }C$
3. $T={90}^{\circ }C$
4. $T={80}^{\circ }C$

Q. A cylindrical rod of aluminium is of length $20$ cms and radius $2$ cms. The two ends are maintained at temperatures of $0^{\circ }C$ and ${50}^{\circ }C$ the coefficient of thermal conductivity is $0.5cal/\left(cm\times sec{\times }^{\circ }C\right)$Then the thermal resistance of the rod in $cal/\left(sec{\times }^{\circ }C\right)$ is

1. 318
2. 31.8
3. 3.18
4. 0.318