$A$ 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 $\alpha$.

$A$ solid cube of mass $m$ at a temperature $\theta_0$ is heated at a constant rate. It becomes liquid at temperature $\theta_1$ and vapour at temperature $\theta_2$. Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively,then the minimum heat energy supplied to the cube until it vaporises is

$1 \ gm$ of ice at $0^o C$ is mixed with $1 \ gm$ of steam at $100^o C$. What will be the final temperature $(^o C)$?

$A$ liquid at $30^{\circ} C$ is poured very slowly into a calorimeter at $110^{\circ} C$. The boiling point of the liquid is $80^{\circ} C$. It is observed that the first $5 \ gm$ of the liquid evaporates completely. After adding another $80 \ gm$ of the liquid,the equilibrium temperature is found to be $50^{\circ} C$. What is the ratio of the latent heat of the liquid to its specific heat? [Neglect heat exchange with the surroundings]

$A$ 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

$A$ bullet of mass $m$ moving with a uniform velocity $v$ stops suddenly after hitting a target. If the whole mass melts,given the specific heat $S$,initial temperature $25^{\circ}C$,melting point $475^{\circ}C$,and latent heat $L$,then $v$ is given by: