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 $\dfrac{3}{4}\lambda_0.$ The power radiated by it now becomes $nP.$ The value of $n$ is:

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. $1800$

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:
             

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 $100~^{\circ}\text{C},$ while the other one is at $0~^{\circ}\text{C}.$ If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is:

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:

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. $\alpha_1L_2=\alpha_2L_1$