The coefficient of area expansion ββ of a rectangular sheet of a solid in terms of the coefficient of linear expansion α is:
1. 2α
2. α
3. 3α
4. α2
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
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−1K−1 and the specific heat capacity of water sw=4.18×103 J kg−1K−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
When 0.15 kg of ice at 0∘C is mixed with 0.30 kg of water at 50∘C in a container, the resulting temperature is 6.7∘C.
The heat of fusion of ice is: (Swater=4186 J kg–1 K–1)
1. 3.43×104 Jkg–1
2. 3.34×104 Jkg–1
3. 3.34×105 Jkg–1
4. 4.34×105 Jkg–1
1. | 9.1×107 J | 2. | 8.1×106 J |
3. | 9.1×106 J | 4. | 8.1×107 J |
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−1m−1K−1; and of copper =385 J s−1m−1K−1).
An iron bar
(L1=0.1m,A1=0.02 m2,K1=79 Wm−1K−1) and a brass bar
(L2=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
An iron bar K1=79 W m−1K−1 and a brass bar K2=109 W m−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. Then the equivalent thermal conductivity of the compound bar is:
1. | 94.6 W m−1K−1 | 2. | 93.6 W m−1K−1 |
3. | 81.6 W m−1K−1 | 4. | 91.6 W m−1K−1 |
An iron bar (L1=0.1 m,A1=0.02 m2,K1=79 W m−1K−1) and a brass bar (L2=0.1 m,A2=0.02 m2,K2=109 W m−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 heat current through the compound bar is:
1. 916.1 W
2. 826.1 W
3. 926.1 W
4. 726 W