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. \( \frac{81}{256}\)

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at \(100~^{\circ}\mathrm{C}\), while the other one is at \(0~^{\circ}\mathrm{C}.\) 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:

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

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. \(\alpha_1L_2=\alpha_2L_1\)

The value of the coefficient of volume expansion of glycerine is \(5\times10^{-4} \mathrm{~K^{-1}}\). The fractional change in the density of glycerine for a rise of \(40^\circ \text{C}\) in its temperature is:$\mathrm{}$
1. \(0.015\)
2. \(0.020\)
3. \(0.025\)
4. \(0.010\)

On observing light from three different stars \(P\), \(Q\), and \(R\), it was found that the intensity of the violet colour is maximum in the spectrum of \(P\), the intensity of the green colour is maximum in the spectrum of \(R\) and the intensity of the red colour is maximum in the spectrum of \(Q\). If \(T_P\), \(T_Q\), and \(T_R\) are the respective absolute temperatures of \(P\), \(Q\), and \(R\), then it can be concluded from the above observations that:
1. \(T_P>T_Q>T_R\)
2. \(T_P>T_R>T_Q\)
3. \(T_P<T_R<T_Q\)
4. \(T_P<T_Q<T_R\)

The two ends of a metal rod are maintained at temperatures \(100~^\circ\text{C}\) and \(110~^\circ\text{C}.\) The rate of heat flow in the rod is found to be \(4.0\) J/s. If the ends are maintained at temperatures \(200~^\circ \text{C}\) and \(210 ~^\circ \text{C},\) 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