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. \(\alpha^2\)

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: $\mathrm{\alpha } \mathrm{for} \mathrm{iron}=1.20\times {10}^{-5} °{\mathrm{C}}^{-1}$)

1.   $128 °\mathrm{C}$

2.   $118 °\mathrm{C}$

3.   $227 °\mathrm{C}$ 

4.   $218 °\mathrm{C}$

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 = $0.386\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and 

the specific heat capacity of water $\left({\mathrm{s}}_{\mathrm{w}}\right) = 4.18\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

1.   $1.811 \mathrm{kJ} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$

2.   $1.911 \mathrm{kJ} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$

3.   $0.811 \mathrm{kJ} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$

4.   $0.911 \mathrm{kJ} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$

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 = $2100 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$, the specific heat capacity of water = $4186 {\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, the latent heat of fusion of ice = $3.35\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$
and the latent heat of steam = $2.256\times {10}^6 \mathrm{J} {\mathrm{kg}}^{-1}$.)

1.  $9.1\times {10}^7 \mathrm{J}$

2.  $8.1\times {10}^6 \mathrm{J}$

3.  $9.1\times {10}^6 \mathrm{J}$

4.  $8.1\times {10}^7 \mathrm{J}$

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 = $50.2 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$; and of copper = $385 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$).

1.  $44.4 °\mathrm{C}$

2.  $44.4 \mathrm{K}$

3.  $54.4 °\mathrm{C}$

4.  $54.4 \mathrm{K}$

An iron bar $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1=0.02 {\mathrm{m}}^2, {\mathrm{K}}_1=79 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ and a brass bar$\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 {\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right)$ 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.  $215 \mathrm{K}$

2.  $315 \mathrm{K}$

3.  $415 \mathrm{K}$

4.  $115 \mathrm{K}$

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 \(69^{\circ}\mathrm{C}\)?

An iron bar $\left({\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ 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 and the  The equivalent thermal conductivity of the compound bar is:

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

2.  $93.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

3.  $81.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

4.  $91.6 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}$

An iron bar $\left({\mathrm{L}}_1 = 0.1 \mathrm{m}, {\mathrm{A}}_1 0.02 {\mathrm{m}}^2, {\mathrm{K}}_1 = 79 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ and a brass bar $\left({\mathrm{L}}_2 = 0.1 \mathrm{m}, {\mathrm{A}}_2 = 0.02 {\mathrm{m}}^2, {\mathrm{K}}_2 = 109 \mathrm{W} {\mathrm{m}}^{-1} {\mathrm{K}}^{-1}\right)$ 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.  $916.1 \mathrm{W}$

2.  $826.1 \mathrm{W}$

3.  $926.1 \mathrm{W}$

4.  $726 \mathrm{W}$