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

Steam at \(100~^{\circ}\mathrm{C}\) is passed into \(20~\text{g}\) of water at \(10~^{\circ}\mathrm{C}\). When water acquires a temperature of \(80~^{\circ}\mathrm{C}\), the mass of water present will be: 
[Take specific heat of water \(= 1~\text{cal g}^{-1}~^\circ\mathrm{C}^{-1}\) and latent heat of steam \(= 540~\text{cal g}^{-1}\)]
1. \(24~\text{g}\)
2. \(31.5~\text{g}\)
3. \(42.5~\text{g}\)
4. \(22.5~\text{g}\)

A certain quantity of water cools from \(70~^{\circ}\text{C}\) to \(60~^{\circ}\text{C}\) in the first \(5\) minutes and to \(54~^{\circ}\text{C}\) in the next \(5\) minutes. The temperature of the surroundings is:
1. \(45~^{\circ}\text{C}\)
2. \(20~^{\circ}\text{C}\)
3. \(42~^{\circ}\text{C}\)
4. \(10~^{\circ}\text{C}\)