\(100\) g water at \(20^\circ\text{C}\) is mixed with \(300\) g water at \(100^\circ\text{C}\) in a calorimeter. The mixture is now mixed again with \(400\) g water at \(10^\circ\text{C}.\) The final temperature of the mixture, assuming no loss of heat, is:
1. \(16^\circ\text{C}\)
2. \(30^\circ\text{C}\)
3. \(40^\circ\text{C}\)
4. \(45^\circ\text{C}\)

A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:

The ice-point reading on a thermometer scale is found to be \(20^\circ,\) while the steam point is found to be \(70^\circ.\) When this thermometer reads \(100^\circ ,\) the actual temperature is:
1. \(80^\circ\text{C}\)
2. \(130^\circ\text{C}\)
3. \(160^\circ\text{C}\)
4. \(200^\circ\text{C}\)

A gas thermometer measures the temperature by measuring the pressure of a constant volume of gas (considered to be ideal). The pressure is directly proportional to the absolute temperature. The pressure at \(27^\circ\text{C}\) is found to be \(15\) kPa. When the pressure is \(20\) kPa, the temperature is:
1. \(20.25^\circ\text{C}\)
2. \(127^\circ\text{C}\)
3. \(225^\circ\text{C}\)
4. \(36^\circ\text{C}\)

The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:

Two rods of identical dimensions are joined end-to-end, and the ends of the composite rod are kept at \(0^\circ\text{C}\) and \(100^\circ\text{C}\) (as shown in the diagram). The temperature of the joint is found to be \(40^\circ\text{C}.\) Assuming no loss of heat through the sides of the rods, the ratio of the conductivities of the rods \(\dfrac{K_1}{K_2}\) is:

A metal ball of mass \(2\) kg is heated by a \(30~\text{W}\) heater, in a room at \(20^{\circ}\text{C}\). The temperature of the metal becomes steady at \(50^{\circ}\text{C}\). The rate of loss of heat from the ball when the temperature is \(50^{\circ}\text{C}\) is:
1. \(0~\text{W}\)
2. \(50~\text{W}\)
3. \(25~\text{W}\)
4. \(30~\text{W}\)

A metal ball of mass \(2\) kg is heated by a \(30\) W heater, in a room at \(20^\circ \text{C}.\) The temperature of the metal becomes steady at \(50^\circ \text{C}.\) If the same ball was heated by a \(20\) W heater in a room at \(30^\circ \text{C},\) the steady temperature of the ball will be:

A metal ball of mass \(2~\text{kg}\) is heated by a \(30~\text{W}\) heater, in a room at \(20^{\circ}\text{C}.\) The temperature of the metal becomes steady at \(50^{\circ}\text{C}.\) If the ball was kept in a room at \(20^{\circ}\text{C}\) while maintaining a temperature of \(10^{\circ}\text{C},\) the rate at which heat must be removed from the ball is:
1. \(20~\text{W}\)
2. \(10~\text{W}\)
3. \(5~\text{W}\)
4. \(1~\text{W}\)