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 °C. To what temperature should the ring be heated so as to fit the rim of the wheel?

(Given: α for iron=1.20×10-5 °C-1)

1.   128 °C

2.   118 °C

3.   227 °C 

4.   218 °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 °C. It is then immediately transferred to a 0.14 kg copper calorimeter containing 0.25 kg water at 20 °C. The temperature of water rises and attains a steady-state at 23 °C. The specific heat capacity of aluminium is:

(Given that: Specific heat capacity of copper calorimeter = 0.386×103 J kg-1 K-1 and 

the specific heat capacity of water sw = 4.18×103 J kg-1 K-1)

1.   1.811 kJ kg-1K-1

2.   1.911 kJ kg-1K-1

3.   0.811 kJ kg-1K-1

4.   0.911 kJ kg-1K-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 |
 58%
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The heat required to convert 3 kg of ice at –12 °C kept in a calorimeter to steam at 100 °C at atmospheric pressure is:

(Given, the specific heat capacity of ice = 2100 J kg-1K-1, the specific heat capacity of water = 4186 Jkg-1K-1, the latent heat of fusion of ice = 3.35×105 J kg-1
and the latent heat of steam = 2.256×106 J kg-1.)

1.  9.1×107 J

2.  8.1×106 J

3.  9.1×106 J

4.  8.1×107 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 °C, temperature of the other end = 0 °C. The area of the cross section of the steel rod is twice that of the copper rod.

(Thermal conductivity of steel = 50.2 J s-1 m-1 K-1; and of copper = 385 J s-1 m-1 K-1).

1.  44.4 °C

2.  44.4 K

3.  54.4 °C

4.  54.4 K

Subtopic:  Conduction |
 57%
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An iron bar L1 = 0.1 m, A1=0.02 m2, K1=79 Wm-1K-1 and a brass barL2 = 0.1 m, A2 = 0.02 m2, K2 = 109 Wm-1K-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. 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 \(94^{\circ}\mathrm{C}\) to \(86^{\circ}\mathrm{C}\) when the room temperature is \(20^{\circ}\mathrm{C}\). How long will it take to cool from \(71^{\circ}\mathrm{C}\) to \(69^{\circ}\mathrm{C}\)?

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 K1 = 79 W m-1 K-1 and a brass bar K2 = 109 W m-1 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 and the  The equivalent thermal conductivity of the compound bar is:

1.  94.6 W m-1 K-1

2.  93.6 W m-1 K-1

3.  81.6 W m-1 K-1

4.  91.6 W m-1 K-1

Subtopic:  Conduction |
 63%
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An iron bar L1 = 0.1 m, A1 0.02 m2, K1 = 79 W m-1 K-1 and a brass bar L2 = 0.1 m, A2 = 0.02 m2, K2 = 109 W m-1 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. 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 |
 63%
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