If $1\; g$ of steam at $100^{\circ}C$ is mixed with $1\; g$ of ice at $0^{\circ}C$,then the resultant temperature of the mixture is ........ $^{\circ}C$.

Which of the following best represents the temperature versus heat supplied graph for water,in the range of $-20^{\circ}C$ to $120^{\circ}C$?

The pressure applied from all directions on a cube is $P$. How much should its temperature be raised to maintain the original volume? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$.

$A$ 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]

$A$ calorimeter of mass $0.2 \ kg$ and specific heat $900 \ J/kg \cdot K$ contains $0.5 \ kg$ of a liquid of specific heat $2400 \ J/kg \cdot K$. Its temperature falls from $60^{\circ}C$ to $55^{\circ}C$ in one minute. The rate of cooling is ....... $J/s$.

$A$ waterfall is $84 \ m$ high. If half of the potential energy of the falling water gets converted to heat,the rise in temperature of the water will be: (in $^\circ C$)