A brass wire \(1.8~\text m\) long at \(27^\circ \text C\) is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of \(-39^\circ \text C,\) what is the tension created in the wire?
( Assume diameter of the wire to be \(2.0~\text{mm}\) , coefficient of linear expansion of brass \(=2.0 \times10^{-5}~\text{K}^{-1},\) Young's modulus of brass\(=0.91 \times10^{11}~\text{Pa}\) )
1. \(3.8 \times 10^3~\text N\) 
2. \(3.8 \times 10^2~\text N\) 
3. \(2.9 \times 10^{-2}~\text N\) 
4. \(2.9 \times 10^{2}~\text N\) 

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. \(\alpha^2\)

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 temperature of water at the surface of a deep lake is \(2^{\circ} ~\text{C}.\) The temperature expected at the bottom is:
1. \(0^{\circ} \mathrm{C}\)
2. \(2^{\circ} \mathrm{C}\)
3. \(4^{\circ} \mathrm{C}\)
4. \(6^{\circ} \mathrm{C}\)

In a room containing air, heat can go from one place to another:
1. by conduction only
2. by convection only
3. by radiation only
4. by all three modes

A solid at temperature \(T_1\), is kept in an evacuated chamber at temperature \(T_2>T_1\). The rate of increase of temperature of the body is proportional to:
1. \(T_2-T_1\)
2. \(T^2_2 -T^2_1 \)
3. \(T^3_2 -T^3_1\) 
4. \(T^4_2 -T^4_1\)

A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:

The ice-point reading on a thermometer scale is found to be \(20^\circ,\) while the steam point is found to be \(70^\circ.\) When this thermometer reads \(100^\circ ,\) the actual temperature is:
1. \(80^\circ\text{C}\)
2. \(130^\circ\text{C}\)
3. \(160^\circ\text{C}\)
4. \(200^\circ\text{C}\)