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: )
1.
2.
3.
4.
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 = and the specific heat capacity of water )
1.
2.
3.
4.
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
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 = , the specific heat capacity of water = , the latent heat of fusion of ice =
and the latent heat of steam = .)
1.
2.
3.
4.
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 = ; and of copper = ).
1.
2.
3.
4.
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
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 |
An iron bar and a brass bar 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.
2.
3.
4.
An iron bar \((L_{1} = 0 . 1 ~ \text m , A_{1} = 0 . 02 ~\text m^{2} , \) \( K_{1} = 79 W m^{- 1} K^{- 1})\) and a brass bar \((L_{2} = 0 . 1 m , A_{2} = 0 . 02 m^{2} , \) \( K_{2} = 109 W m^{- 1} K^{- 1})\) 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
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. \(\alpha^2\)