Water of volume $2\, L$ in a container is heated with a coil of $1\, kW$ at $27 \,^{\circ}C$. The lid of the container is open and energy dissipates at a rate of $160\, J/s$. In how much time will the temperature rise from $27\,^{\circ}C$ to $77\,^{\circ}C$? [Given: specific heat of water is $4.2\, kJ/(kg \cdot K)$]

$A$ pellet of mass $m$ and specific heat capacity $c$ fired from an air gun hits a steel plate with speed $v$. During the impact,$50\%$ of the pellet's kinetic energy is converted to thermal energy in it. The rise in the temperature of the pellet is

$A$ cube is subjected to a pressure $P$ on all its faces at a temperature of $0 \, ^\circ C$. By what temperature should the cube be heated so that it regains its original volume? Let the bulk modulus of the cube be $\beta$ and the coefficient of volume expansion be $\alpha$.

$A$ piece of ice (heat capacity = $2100 \text{ J kg}^{-1} \text{ }^\circ\text{C}^{-1}$ and latent heat = $3.36 \times 10^5 \ J kg^{-1}$) of mass $m$ grams is at $-5^oC$ at atmospheric pressure. It is given $420 \ J$ of heat so that the ice starts melting. Finally, when the ice-water mixture is in equilibrium, it is found that $1 \ gm$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is ...... $gm$.

$A$ thermocouple produces $40 \, \mu V/K$. The temperatures of the cold and hot junctions are $40 \, ^\circ C$ and $20 \, ^\circ C$ respectively. If $150$ such thermocouples are connected in series,what is the total thermo-emf produced in $mV$?

$A$ beaker is filled with water at $4\,^{\circ}C$. At one time the temperature is increased by a few degrees above $4\,^{\circ}C$ and at another time it is decreased by a few degrees below $4\,^{\circ}C$. One shall observe that: