The coefficient of area expansion $$\beta$$ of a rectangular sheet of a solid in terms of the coefficient of linear expansion $$\alpha$$ is:
1. $$2\alpha$$
2. $$\alpha$$
3. $$3\alpha$$
4. $$\alpha^2$$

Subtopic:  Thermal Expansion |
90%
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A blacksmith fixes an iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $$5.012$$ m and $$5.00$$ m, respectively at $$27^{\circ}\text{C}.$$ To what temperature should the ring be heated so as to fit the rim of the wheel?
$$\left(\text{Given:}~\alpha~\text{for iron}= 1.20 \times 10^{-5}~^\circ{\text{C}^{-1}}\right)$$
1. $$128^{\circ}\text{C}$$
2. $$118^{\circ}\text{C}$$
3. $$227^{\circ}\text{C}$$
4. $$218^{\circ}\text{C}$$

Subtopic:  Thermal Expansion |
63%
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A sphere of $$0.047$$ kg aluminium is placed for sufficient time in a vessel containing boiling water so that the sphere is at $$100^{\circ}\text{C}$$. It is then immediately transferred to a $$0.14$$ kg copper calorimeter containing $$0.25$$ kg water at $$20^{\circ}\text{C}$$. The temperature of water rises and attains a steady-state at $$23^{\circ}\text{C}$$. The specific heat capacity of aluminium is:
(Given that: Specific heat capacity of copper calorimeter $$= 0.386\times 10^{3}~\text{J kg}^{-1}\text{K}^{-1}$$ and the specific heat capacity of water $$s_w= 4.18\times 10^{3}~\text{J kg}^{-1}\text{K}^{-1})$$
1. $$1.811~\text{kJ kg}^{-1}\text{K}^{-1}$$
2. $$1.911~\text{kJ kg}^{-1}\text{K}^{-1}$$
3. $$0.811~\text{kJ kg}^{-1}\text{K}^{-1}$$
4. $$0.911~\text{kJ kg}^{-1}\text{K}^{-1}$$

Subtopic:  Calorimetry |
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When $$0.15$$ kg of ice at $$0^\circ \text{C}$$ is mixed with $$0.30$$ kg of water at $$50^\circ \text{C}$$ in a container, the resulting temperature is $$6.7^\circ \text{C}.$$
The heat of fusion of ice is: ($$S_{\text{water}}=4186$$ J kg–1 K–1)
1. $$3.43 \times 10^4$$ Jkg–1
2. $$3.34 \times 10^4$$ Jkg–1
3. $$3.34 \times 10^5$$ Jkg–1
4. $$4.34 \times 10^5$$ Jkg–1

Subtopic:  Calorimetry |
57%
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The heat required to convert $$3$$ kg of ice at $$-12^{\circ}\text{C}$$ kept in a calorimeter to steam at $$100^{\circ}\text{C}$$ at atmospheric pressure is: (Given, the specific heat capacity of ice $$= 2100~\text{J kg}^{-1}\text{K}^{-1},$$ the specific heat capacity of water $$= 4186~\text{J kg}^{-1}\text{K}^{-1},$$ the latent heat of fusion of ice $$= 3.35\times 10^{5}~\text{J kg}^{-1}$$${}^{}$
and the latent heat of steam $$= 2.256\times 10^6~\text{J kg}^{-1}.)$$
1. $$9.1\times 10^{7}~\text{J}$$
2. $$8.1\times 10^{6}~\text{J}$$
3. $$9.1\times 10^{6}~\text{J}$$
4. $$8.1\times 10^{7}~\text{J}$$
Subtopic:  Calorimetry |
62%
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What is the temperature of the steel-copper junction in the steady-state of the system shown in the figure? The length of the steel rod = $$15.0$$ cm, length of the copper rod = $$10.0$$ cm, temperature of the furnace = $$300^{\circ}\text{C}$$, temperature of the other end = $$0^{\circ}\text{C}$$. The area of the cross section of the steel rod is twice that of the copper rod. (Thermal conductivity of steel = $$50.2 ~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1};$$ and of copper $$= 385~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1})$$.

1. $$44.4^{\circ}\text{C}$$
2. $$44.4~\text{K}$$
3. $$54.4^{\circ}\text{C}$$
4. $$54.4~\text{K}$$

Subtopic:  Conduction |
56%
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An iron bar $$\left(L_{1} = 0 . 1 m , A_{1} = 0 . 02 m^{2} , K_{1} = 79 W m^{- 1} K^{- 1}\right)$$ and a brass bar $$\left(L_{2} = 0 . 1 m , A_{2} = 0 . 02 m^{2} , K_{2} = 109 W m^{- 1} K^{- 1}\right)$$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at 373 K and 273 K respectively. The temperature of the junction of the two bars is:

1.  215 K

2. 315 K

3. 415 K

4.115 K

Subtopic:  Conduction |
78%
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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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An iron bar $$K_1 = 79~\text{W m}^{-1}\text{K}^{-1}$$ and a brass bar $$K_2 = 109~\text{W m}^{-1}\text{K}^{-1}$$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at $$373$$ K and $$273$$ K respectively. Then the equivalent thermal conductivity of the compound bar is:

1. $$94.6~\text{W m}^{-1}\text{K}^{-1}$$

2. $$93.6~\text{W m}^{-1}\text{K}^{-1}$$
3. $$81.6~\text{W m}^{-1}\text{K}^{-1}$$
4. $$91.6~\text{W m}^{-1}\text{K}^{-1}$$
Subtopic:  Conduction |
62%
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An iron bar $$\left(L_{1} = 0 . 1 ~ \text{m}, A_{1} = 0 . 02 ~\text{m}^{2}, K_{1} = 79~\text{W m}^{- 1} \text{K}^{- 1}\right)$$ and a brass bar $$\left(L_{2}= 0 . 1 ~\text{m}, A_2 = 0.02~\text{m}^2, K_2 = 109~\text{W m}^{-1}\text{K}^{-1}\right)$$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at $$373$$ K and $$273$$ K respectively. The heat current through the compound bar is:

1. $$916.1$$ W
2. $$826.1$$ W
3. $$926.1$$ W
4. $$726$$ W

Subtopic:  Conduction |
62%
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