A copper ball of mass \(100~\text{gm}\) is at a temperature \(T.\) It is dropped in a copper calorimeter of mass \(100~\text{gm},\) filled with \(170~\text{gm} \) of water at room temperature. Subsequently, the temperature of the system is found to be \(75^\circ\text{C}. \) \(T\) is given by: (Given: room temperature = \(30^\circ \text{C}, \) specific heat of copper = \(0.1~\text{cal}/ \text{g}~^\circ\text{C}) \)
1. \( 800^{\circ} \text{C} \)
2. \(885^{\circ} \text{C} \)
3. \(1250^{\circ} \text{C} \)
4. \( 825^{\circ} \text{C}\)

A thermally insulated vessel contains \(150~\text{g}\) of water at \(0^\circ\text{C}\). Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at \(0^\circ\text{C}\) itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water =\(2.10 \times 10^6 ~\text{Jkg}^{-1}\) and Latent heat of fusion of water = \(3.36 \times 10^5 ~\text{Jkg}^{-1}\))
1. \(130~\text{g}\)
2. \(35~\text{g}\)
3. \(150~\text{g}\)
4. \(20~\text{g}\)

When \(M_1\) gram of ice at \(-10^\circ \text{C}\) (specific heat = \(0.5~\text{cal g}^{-1} ~^{\circ}\text{C}^{-1}\)) is added to \(M_2\) gram of water at \(50^\circ \text{C}\), It is observed that no ice is left and the water is at \(0^\circ \text{C}\). The value of latent heat of ice, in \(\text{cal g}^{-1}\) is:
1. \(\frac{50M_2}{M_1}-5\)
2. \(\frac{50M_2}{M_1}\)
3. \(\frac{5M_2}{M_1}-5\)
4. \(\frac{50M_1}{M_2}-5\)

A calorimeter of water equivalent \(20~\text{g}\) contains \(180~\text{g}\) of water at \(25^\circ ~\mathrm{C}\). '\(m\)' grams of steam at \(100^\circ ~\mathrm{C}\) is mixed in it till the temperature of the mixture is  \(31^\circ ~\mathrm{C}\). The value of '\(m\)'(in grams) is close to: (Latent heat of water = \(540~\mathrm{cal ~g^{-1}}\), specific heat of water = \(1~\mathrm{cal ~g^{-1}}^\circ \mathrm{C^{-1}}\))
1. \(2\)
2. \(2.6\)
3. \(4\)
4. \(3.2\)

The specific heat of water = \(4200 ~\text{J} \text{kg}^{-1} \text{K}^{-1}\) and the latent heat of ice = \(3.4 \times 10^5~ \text{J} \text{kg}^{-1}\). \(100\) grams of ice at \(0^\circ\mathrm{C}\) is placed in \(200\) g of water at \(25^\circ\mathrm{C}\). The amount of ice that will melt as the temperature of the water reaches \(0^\circ\mathrm{C}\) is close to (in grams):
1. \(61.7\)
2. \(69.3\)
3. \(64.6\)
4. \(63.8\)

A bullet of mass \(5~\text{g}\), travelling with a speed of \(210~\text{m/s}\), strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is \(0.03 ~\text{cal/gm}^{\circ} \text{C}\) (\(1~\text{cal}=4.2 \times 10^7 \text{ergs}\)) close to:
1. \( 83.3^{\circ} \text{C} \)
2. \(87.5^{\circ}\text{C} \)
3. \(119.2^{\circ} \text{C} \)
4. \(38.4^{\circ} \text{C} \)