# Two conducting slabs of heat conductivity $$K_{1} ~\text{and}~K_{2}$$ are joined as shown in figure. If the temperature at the ends of the slabs are $$\theta_{1}~\text{and}~\theta_{2} \ (\theta_{1} > \theta_{2} ),$$ then the final temperature $$\left(\theta\right)_{m}$$ of the junction will be:                  1. $$\frac{K_{1} \theta_{1} + K_{2} \theta_{2}}{K_{1} + K_{2}}$$ 2. $$\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} + K_{2}}$$ 3. $$\frac{K_{1} \theta_{2} + K_{2} \theta_{1}}{K_{1} - K_{2}}$$ 4. None

Subtopic:  Conduction |
83%
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AIPMT - 1999
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A pan filled with hot food cools in $$2$$ minutes from $$94^{\circ}\text{C}$$ to $$86^{\circ}\text{C}$$ when the room temperature is $$20^{\circ}\text{C}$$. How long will it take to cool from $$71^{\circ}\text{C}$$ to $$69^{\circ}\text{C}$$?
1. $$50$$ sec
2. $$52$$ sec
3. $$42$$ sec
4. $$48$$ sec

Subtopic:  Newton's Law of Cooling |
78%
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A piece of iron is heated in a flame. If it becomes dull red first, 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 Kirchhoff's law 4 Newton's law of cooling
Subtopic:  Wien's Displacement Law |
81%
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The diagram shows a bimetallic strip used as a thermostat in a circuit. Copper expands more than Invar for the same temperature rise.

What will be switched on when the bimetallic strip becomes hot?

 1 bell only 2 lamp and bell only 3 motor and bell only 4 lamp, bell, and motor

Subtopic:  Thermal Expansion |
From NCERT
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In an experiment on the specific heat of a metal, a $$0.20$$ kg block of the metal at $$150^{\circ}\text{C}$$ is dropped in a copper calorimeter (of water equivalent of $$0.025$$ kg) containing $$150~\text{cm}^{3}$$ of water at $$27^{\circ}\text{C}$$. The final temperature is $$40^{\circ}\text{C}$$. The specific heat of the metal will be:
(Heat losses to the surroundings are negligible)
1. $$0 . 40 ~ \text{Jg}^{- 1} \text{K}^{- 1}$$
2. $$0 . 43 ~ \text{Jg}^{- 1} \text{K}^{- 1}$$
3. $$0 . 54 ~ \text{Jg}^{- 1} \text{K}^{- 1}$$
4. $$0 . 61 ~ \text{Jg}^{- 1} \text{K}^{- 1}$$

Subtopic:  Calorimetry |
60%
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A brass wire $$1.8$$ m long at $$27$$ °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of$$-39$$ °C, what is the tension created in a wire with a diameter of $$2.0$$ mm? (coefficient of linear expansion of brass $$=2.0 \times10^{-5}$$ K–1, Young's modulus of brass$$=0.91 \times10^{11}$$ Pa)
1. $$3.8 \times 10^3$$ N
2. $$3.8 \times 10^2$$ N
3. $$2.9 \times 10^{-2}$$ N
4. $$2.9 \times 10^{2}$$ N

Subtopic:  Thermal Stress |
67%
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Two absolute scales $$A$$ and $$B,$$ have triple points of water defined to be $$200 A$$ and $$350 B$$. The relationship between $$T_A$$ and $$T_B$$:
1. $$T_A = {5 \over 7}T_B$$
2. $$T_A = { 4 \over 7}T_B$$
3. $$T_A = { 6 \over 7}T_B$$
4. $$T_A = T_B$$
Subtopic:  Temperature and Heat |
73%
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5 g of water at $$30^{\circ} \mathrm{C}$$ and 5 g of ice at $$-20^{\circ} \mathrm{C}$$ are mixed together in a calorimeter. The water equivalent of the calorimeter is negligible, and the specific heat and latent heat of ice are 0.5 $$\text{cal/g}^{\circ} \mathrm{C}$$ and 80 $$\text{cal/g}$$, respectively. The final temperature of the mixture is:

 1 $$0^{\circ} \mathrm{C}$$ 2 $$-8^{\circ} \mathrm{C}$$ 3 $$-4^{\circ} \mathrm{C}$$ 4 $$2^{\circ} \mathrm{C}$$
Subtopic:  Calorimetry |
72%
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Three rods made of the same material, having the same cross-sectional area but different lengths 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction will be:-

1. $$10.8^{\circ}\mathrm{C}$$
2. $$14.6^{\circ}\mathrm{C}$$
3. $$16.4^{\circ}\mathrm{C}$$
4. $$18.2^{\circ}\mathrm{C}$$

Subtopic:  Conduction |
70%
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Four rods of the same material with different radii $$r$$ and length $$l$$ are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1. $$r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}$$
2. $$r =3~\text{cm}, l =9~\text{cm}$$
3. $$r =4~\text{cm}, l =8~\text{cm}$$
4. $$r =1~\text{cm}, l =1~\text{cm}$$

Subtopic:  Conduction |
73%
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