Conduction Law

Q.

The dimensional formula for thermal conductivity is (here $\mathrm{K}$ denotes the temperature):

1. $ML{T}^{-3}{K}^{-1}$

2. $ML{T}^{-2}{K}^{-2}$

3. $ML{T}^{-2}K$

4. $ML{T}^{-3}K$

Q.

What is thermal conductivity connected in parallel and series?

Q.

SI unit of thermal conductivity is

Q.

The thermal conductivity of a rod depends on

1. Length

2. Mass

3. Area of cross section

4. Material of the rod

Q. A furnace is made of a red brick wall of thickness $0.5\text{m}$ and conductivity $0.7\text{W/mK}$. For the same rate of heat conduction and the same temperature drop, this can be replaced by a diatomite wall of conductivity $0.14\text{W/mK}$ and the same cross-sectional area. Find the thickness of the diatomite wall.

1. $0.05\text{m}$
2. $0.1\text{m}$
3. $0.2\text{m}$
4. $0.5\text{m}$

Q. A cylinder of radius $R$ made of material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $3R$ made of a material of thermal conductivity $K_2$. The two ends of a combined systems are maintained at two different temperatures. What is the thermal conductivity of the system?

1. $K_1+K_2$
2. $\frac{K_1+8K_2}{9}$
3. $\frac{K_1{K}_2}{K_1+K_2}$
4. $\frac{8K_1+K_2}{9}$

Q. In the figure shown below, two rods are maintained at the same temperature difference between the ends. As a result, heat is flowing through two rods made of the same material. If the diameters of the rods are in the ratio $1:4$ and their lengths are in the ratio $3:2$, then find the ratio of the rates of flow of heat through them.

1. $1:24$
2. $1:8$
3. $1:4$
4. $1:6$

Q. The ends of copper rod of length $1\text{m}$ and area of cross section $1{\text{cm}}^2$ are maintained at $0^{\circ }C$ and ${100}^{\circ }C$. At the centre of the rod there is a source of heat of power $25\text{W}$. Thermal conductivity of copper is $400\text{W/m-K}$. In steady state, the temperature at the section of rod at which source is supplying heat, will be

1. ${150.50}^{\circ }C$
2. ${325.75}^{\circ }C$
3. ${206.25}^{\circ }C$
4. ${126.25}^{\circ }C$

Q. Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_1$ and $T_2$, rod $1$ takes twice the time as the other. Find the ratio of their lengths.

1. $2:1$
2. $1:3$
3. $1:1$
4. $\sqrt{2}:1$

Q. A plane wall is $25\text{cm}$ thick with an area of $1{\text{m}}^2$ and has a thermal conductivity of $0.5\text{W/mK}$. If a temperature difference of ${60}^{\circ }\text{C}$ is maintained across it, then find the rate of heat flow.

1. $120\text{W}$
2. $140\text{W}$
3. $160\text{W}$
4. $180\text{W}$

Q. If the sides of a wall having thermal conductivity $K$ are maintained at temperatures of $T_1$ and $T_2$, the temperature as a function of $x$ can be written as $T\left(x\right)=(T_2-T_1)\left(\frac{x}{L}\right)+T_1$
Find the heat flux through the wall.
Take $T_1>T_2$

1. $\frac{K{T}_1}{L}$
2. $\frac{K{T}_2}{L}$
3. $\frac{K(T_1-T_2)}{L}$
4. $0$

Q. A rod of length $l$ made of material of thermal conductivity $k$ can transfer a given amount of heat in $12\text{seconds}$. If the length of the rod is doubled keeping the volume constant, it is noted that rod can transfer same heat in $t\text{seconds}$. Find the value of ${}^{\prime }{t}^{\prime }$.

1. $12$
2. $24$
3. $36$
4. $48$

Q.

Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperatures 200${}^{\circ }$C and 20 ${}^{\circ }$ C respectively. Find the temperature of junction B.

1. 120 deg C

2. 140 deg C

3. 160 deg C

4. 180 deg C

Q. Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_1$ and $T_2$, rod $1$ takes twice the time as the other. Find the ratio of their lengths.

1. $2:1$
2. $1:3$
3. $1:1$
4. $\sqrt{2}:1$

Q. In a steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are ${100}^{\circ }$ C and $0^{\circ }$ C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod

1. $-{30}^{\circ }C$
2. ${70}^{\circ }C$
3. $5^{\circ }C$
4. None of the above

Q.

When a coil of copper is kept at a certain distance above a flame, the candle keeps burning, but when the coil is placed over the flame, it is extinguished. This happens because

1. the coil reduces the amount of oxygen necessary for burning

2. the coil prevents the setting up of convection currents in air

3. the coil reduces the radiation losses

4. the coil conducts away heat very quickly and reduces the temperature of the flame to a value below the ignition temperature

Q. Two rods $A$ and $B$ of different materials but same cross section are joined as shown in figure. The free end of $A$ is maintained at ${100}^{\circ }C$ and the free end of $B$ is maintained at $0^{\circ }C$. If $l_2=2l_1,K_1=2K_2$ and rods are thermally insulated from sides to prevent heat losses, then the temperature $\theta$ of the junction of the two rods is

1. ${80}^{\circ }C$
2. ${60}^{\circ }C$
3. ${40}^{\circ }C$
4. ${20}^{\circ }C$

Q. Five identical rods are joined as shown in figure. Point A and C are maintained at temperature ${120}^{\circ }$ C and ${20}^{\circ }$ C respectively. The temperature of junction B will be

1. ${100}^{\circ }$ C
2. ${80}^{\circ }$ C
3. ${70}^{\circ }$ C
4. $0^{\circ }$ C

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. In a kitchen experiment, you empty a tray of ice cubes into a bowl of water. After an hour or so, when the mixture has come to thermal equilibrium, you notice a little more water in the bowl than you started with and fewer ice cubes in the bowl than you started with. One can say that

1. the temperature of the water is slightly higher than the remaining ice cubes
2. the temperature of the water is slightly lower than the remaining ice cubes
3. the temperature of the water is the same as the temperature of the remaining ice cubes
4. the temperature of the water or the ice cubes depends on the exact mass of water and ice cubes in the bowl

Q. A lake is covered with ice and the atmospheric temperature above the ice is $-{20}^{\circ }\text{C}$. Find the rate of formation of ice $\left(\text{in cm/hr}\right)$ when its thickness is $10\text{cm}$.
[Thermal conductivity of ice $=0.005\text{cgs}$ units, density of ice $=0.9\text{g/cc}$ and latent heat of fusion of ice $=80\text{cal/g}$].

1. $50{\text{cm hr}}^{-1}$
2. $25{\text{cm hr}}^{-1}$
3. $0.5{\text{cm hr}}^{-1}$
4. $0.25{\text{cm hr}}^{-1}$

Q. Assuming steady state one-dimensional heat conduction in a composite slab, if $T_{inter}=\frac{T_1+T_2}{2},$ then which of the following statements is true about the respective thermal conductivities?

1. $2K_1=K_2$
2. $K_1=K_2$
3. $2K_1=3K_2$
4. $K_1=2K_2$

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. The ends of a rod of uniform thermal conductivity are maintained at different (constant) temperatures. After the steady state is achieved:

1. Heat flows in the rod from high temperature to low temperature even if the rod has a non-uniform cross sectional area.
2. Temperature gradient along the length is the same even if the rod has non-uniform cross-sectional area.
3. Heat current is same even if the rod has non-uniform cross-sectional area.
4. If the rod has uniform cross-sectional area, the temperature is the same at all points of the rod.

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. $\frac{A_1}{A_2}$$=\frac{K_1}{K_2}$

2. $\frac{A_1}{A_2}$ $=\frac{K_2}{K_1}$

3. $\frac{A_1}{A_2}$ $=\frac{K_1\theta 1}{K_2{\theta }_2}$

4. $\frac{A_1}{A_2}$ $=\frac{K_2{\theta }_2}{K_1{\theta }_1}$

Q. A body takes T minutes to cool from ${62}^{\circ }$ C to${61}^{\circ }$ C when the surrounding temperature is ${30}^{\circ }$ C .The time taken by the body to cool from ${46}^{\circ }$ C to ${45.5}^{\circ }$ C is

1. Greater than T minutes
2. Equal to T minutes
3. Less than T minutes
4. Equal to T/2 minutes

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. $T={80}^{\circ }C$
4. $T={90}^{\circ }C$

Q. Four rods of same material but different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct heat fastest?

1. $r=2\text{cm},l=0.5\text{m}$
2. $r=1\text{cm},l=0.5\text{m}$
3. $r=2\text{cm},l=2\text{m}$
4. $r=1\text{cm},l=1\text{m}$

Q.

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

1. $J{s}^{-1}{m}^{-1}{K}^{-1}$

2. $N{s}^{-2}{m}^{-1}{K}^{-1}$

3. $N{s}^{-1}{m}^{-2}{K}^{-1}$

4. $W{m}^{-1}{K}^{-1}$

Q. A particle is moved from $(0,0)$ to $(a,a)$ under a force $\overrightarrow{F}=3\hat{i}+4\hat{j}$ from two paths. Path $1$ is $OP$ and Path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths. Then

1. $W_2=2W_2$
2. $W_2=4W_1$
3. $W_1=2W_2$
4. $W_1=W_2$