$A$ lead bullet of $20 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50 \%$ of heat is absorbed by the bullet,the increase in its temperature is $.....^{\circ} C$ (take specific heat of lead $= 150 \ J/kg \cdot K$).

Which of the following graphs shows the variation of thermoelectric power of a thermocouple with the temperature difference between the hot and cold junctions?

Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$. The specific heat of ice is $2222.3\,J\,kg^{-1\circ}C^{-1}$ and the latent heat of fusion of ice is $336\,kJ\,kg^{-1}$.
$(A)$ Final temperature of the system will be $0^{\circ}C$.
$(B)$ Final temperature of the system will be greater than $0^{\circ}C$.
$(C)$ The final system will have a mixture of ice and water in the ratio of $5:1$.
$(D)$ The final system will have a mixture of ice and water in the ratio of $1:5$.
$(E)$ The final system will have water only.
Choose the correct answer from the options given below:

$A$ water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure),the water from the cooler is used to cool an external device that generates constantly $3 \text{ kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ}\text{C}$ and the entire stored $120$ litres of water is initially cooled to $10^{\circ}\text{C}$. The entire system is thermally insulated. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is (Specific heat of water is $4.2 \text{ kJ kg}^{-1} \text{K}^{-1}$ and the density of water is $1000 \text{ kg m}^{-3}$)

$A$ continuous flow water heater (geyser) has an electrical power rating $= 2 \, kW$ and efficiency of conversion of electrical power into heat $= 80 \%$. If water is flowing through the device at the rate of $100 \, cc/sec$,and the inlet temperature is $10^{\circ} C$,the outlet temperature will be ....... $^{\circ} C$.

One quality of a thermometer is that its heat capacity should be small. If $P$ is a mercury thermometer,$Q$ is a resistance thermometer,and $R$ is a thermocouple type,then: