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A body of length 1m having cross sectional area 0.75 $m^{2}$ has heat flow through it at the rate of 6000 Joule/sec. Then find the temperature difference if K = 200 ${Jm}^{- 1} K^{- 1}$

20°C

40°C

80°C

100°C

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Explanation

(b)

$\frac{Q}{t} = \frac{KA ∆ θ}{l} \Rightarrow 6000 = \frac{200 \times 0.75 \times ∆ θ}{1} ∴ ∆ θ = \frac{6000 \times 1}{200 \times 0.75} = 40 ° C$

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A wall has two layers A and B made of different materials. The thickness of both the layers is the same. The thermal conductivity of A and B are $K_{A}$ and $K_{B}$ such that $K_{A}$ = 3 $K_{B}$ . The temperature across the wall is 20°C. In thermal equilibrium

The temperature difference across A = 15°C

The temperature difference across A = 5°C

The temperature difference across A is 10°C

The rate of transfer of heat through A is more than that through B.

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Explanation

(b) In series rate of flow of heat is same

$\Rightarrow \frac{K_{A} A (θ_{1} - θ)}{l} = \frac{K_{B} A (θ - θ_{2})}{l} \Rightarrow 3 K_{B} (θ_{1} - θ) = K_{B} (θ - θ_{2}) \Rightarrow 3 (θ_{1} - θ) = (θ - θ_{2}) \Rightarrow 3 θ_{1} - 3 θ = θ - θ_{2} \Rightarrow 4 θ_{1} - 4 θ = θ_{1} - θ_{2} \Rightarrow 4 (θ_{1} - θ) = (θ_{1} - θ_{2}) \Rightarrow 4 (θ_{1} - θ) = 20 \Rightarrow (θ_{1} - θ) = 5 ° C$

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The ratio of the coefficient of thermal conductivity of two different materials is 5 : 3. If the thermal resistance of the rod of same thickness resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be

3 : 5

5 : 3

3 : 4

3 : 2

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Explanation

(b) Thermal resistances are same

$\Rightarrow \frac{l_{1}}{K_{1} A_{1}} = \frac{l_{2}}{K_{2} A_{2}} \Rightarrow \frac{l_{1}}{K_{1}} = \frac{l_{2}}{K_{2}} (∵ A_{1} = A_{2}) \Rightarrow \frac{l_{1}}{l_{2}} = \frac{K_{1}}{K_{2}} = \frac{5}{3}$

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Which of the following circular rods (given radius r and length l) each made of the same material as whose ends are maintained at the same temperature will conduct most heat ?

$r = 2 r_{0}; l = 2 l_{0}$

$r = 2 r_{0}; l = l_{0}$

$r = r_{0}; l = l_{0}$

$r = r_{0}; l = 2 l_{0}$

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Explanation

(b) $\frac{Q}{t} \propto \frac{r^{2}}{l}$ ; from the given options, option (b) has higher value of $\frac{r^{2}}{l}$ .

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It is hotter for the same distance over the top of a fire than it is in the side of it, mainly because

Air conducts heat upwards

Heat is radiated upwards

Convection takes more heat upwards

Convection, conduction and radiation all contribute significantly transferring heat upwards

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Explanation

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Air is bad conductor of heat or partly conducts heat, still vacuum is to be placed between the walls of the thermos flask because

It is difficult to fill the air between the walls of thermos flask

Due to more pressure of air, the thermos can get crack

By convection, heat can flow through air

On filling the air, there is no advantage

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Explanation

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While measuring the thermal conductivity of a liquid, we keep the upper part hot and lower part cool, so that

Convection may be stopped

Radiation may be stopped

Heat conduction is easier downwards

It is easier and more convenient to do so

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Explanation

(a) Heat flows from higher temperature to lower temperature. To avoid movement of heat due to convention, the upper part is kept hot and the lower part is kept cool.

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Mode of transmission of heat, in which heat is carried by the moving particles, is

Radiation

Conduction

Convection

Wave motion

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Explanation

Convection is the mode of heat transfer where heat is carried by the moving particles. In liquids and gases, convection occurs due to the bulk movement of the particles themselves. In solids, convection is not possible as the particles are fixed in position.

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In heat transfer, which method is based on gravitation ?

Natural convection

Conduction

Radiation

Stirring of liquids

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Explanation

(a) Natural convection arises due to difference of density at two places and is a consequence of gravity.

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When fluids are heated from the bottom, convection currents are produced because -

Molecular motion of fluid becomes aligned

Molecular collisions take place within the fluid

Heated fluid becomes more dense than the cold fluid above it

Heated fluid becomes less dense than the cold fluid above it

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Explanation

(d) When the heat is transfered to the fluid at bottom, it becomes less dense and moves upwards.

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