The power radiated by a black body is \(P\) and it radiates maximum energy at wavelength ${}_{}$\(\lambda_0\). Temperature of the black body is now changed so that it radiates maximum energy at the wavelength \(\frac{3}{4}\lambda_0\). The power radiated by it now becomes \(nP\). The value of \(n\) is:
1. \( \frac{3}{4} \)
2. \( \frac{4}{3} \)
3. \( \frac{256}{81} \)
4. \( \frac{81}{256}\)

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:

Two rods \(A\) and \(B\) of different materials 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. $\frac{3(K_1+K_2)}{2}$

2. $K_1+K_2$

3. $2(K_1+K_2)$

4. $\frac{K_1+K_2}{2}$

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)

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100 °C, while the other one is at 0 °C. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is:

1. $50°\mathrm{C}$

2. more than $50°\mathrm{C}$

3. less than $50°\mathrm{C}$ but greater than $0°\mathrm{C}$

4. $0°\mathrm{C}$

A body cools from a temperature of 3T to 2T in 10 minutes. The room temperature is T. Assuming that Newton's law of cooling is applicable, the temperature of the body at the end of the next 10 minutes will be:

1.  $\frac{7}{4}\mathrm{T}$

2.  $\frac{3}{2}\mathrm{T}$

3.  $\frac{4}{3}\mathrm{T}$

4.  $\mathrm{T}$

The coefficient 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 \((L_2-L_1)\) remains the same at all temperatures, which one of the following relations holds good?
1. \(\alpha_1L_2^2=\alpha_2L_1^2\)
2. \(\alpha_1^2L_2=\alpha_2^2L_1\)
3. \(\alpha_1L_1=\alpha_2L_2\)
4. \(\alpha_1L_2=\alpha_2L_1\)