Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

   

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

A spherical black body with a radius of \(12\) cm radiates \(450\)-watt power at \(500\) K. If the radius were halved and the temperature doubled, the power radiated in watts would be:
1. \(225\)
2. \(450\)
3. \(1000\)
4. \(1800\)

The coefficients of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\), lengths of brass and steel rods are \(l_1\) and \(l_2\) respectively. If (\(l_2-l_1\)) is maintained the same at all temperatures, Which one of the following relations holds good?
1. \(\alpha_1 l_2^2=\alpha_2l_1^2\)
2. \(\alpha_1^2 l_2=\alpha_2^2l_1\)
3. \(\alpha_1 l_1=\alpha_2l_2\)
4. \(\alpha_1 l_2=\alpha_2l_1\)

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at a wavelength of 250 nm is U₁, at a wavelength of 500 nm is U₂ and that at 1000 nm is U₃. Given Wien's constant $b=2.88\times {10}^6$ $nm-\mathrm{K,\; which<mspace\; width="1em"></mspace>}$of the following is correct?
1. U₃=0       
2. U₁>U₂
3. U₂>U₁     
4. U₁=0

A piece of ice falls from a height \(h\) so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice, and all energy of ice gets converted into heat during its fall. The value of \(h\) is: (Latent heat of ice is \(3.4\times10^5\) J/kg and \(g=10\) N/kg)

The two ends of a metal rod are maintained at temperatures \(100^{\circ}\mathrm{C}\) and \(110^{\circ}\mathrm{C}\). The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures \(200^{\circ}\mathrm{C}\) and \(210^{\circ}\mathrm{C}\), the rate of heat flow will be:
1. 44.0 J/s
2. 16.8 J/s
3. 8.0 J/s
4. 4.0 J/s

A certain quantity of water cools from \(70^{\circ}\mathrm{C}\) to \(60^{\circ}\mathrm{C}\) in the first 5 minutes and to \(54^{\circ}\mathrm{C}\) in the next 5 minutes. 
The temperature of the surroundings will be: 

The temperature of a wire of length \(1~\text{m}\) and an area of cross-section \(1~\text{cm}^2\) is increased from \(0^{\circ} \text {C}\) to \(100^{\circ} \text {C}.\) If the rod is not allowed to increase in length, the force required will be:
\((\alpha = 10^{-5}/ ^{\circ} \text {C} ~\text{and} ~Y = 10^{11} ~\text{N/m}^2)\)

A metal bar of length \(L\) and area of cross-section \(A\) is clamped between two rigid supports. For the material of the rod, it's Young’s modulus is \(Y\) and the coefficient of linear expansion is \(\alpha.\) If the temperature of the rod is increased by \(\Delta t^{\circ} \text{C},\) the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then: