A liquid of density $0.85 \mathrm{g} {\mathrm{cm}}^{-3}$ flows through a calorimeter at the rate of $8.0 {\mathrm{cm}}^3 {\mathrm{s}}^{-1}$. Heat is added by means of a $250 \mathrm{W}$ electric heating coil and a temperature difference of $15° \mathrm{C}$ is established in steady-state conditions between the inflow and the outflow points of the liquid. The specific heat for the liquid will be ($1 \mathrm{kcal} =4186 \mathrm{J}$ )

The densities of wood and benzene at $0{}^{\circ }\mathrm{C}$ are $880 \mathrm{kg} {\mathrm{m}}^{-3}$ and $900 \mathrm{kg} {\mathrm{m}}^{-3}$, respectively, The coefficients of volume expansion of wood is $1.2\times {10}^{-3}/{}^{\circ }\mathrm{C}$ and of benzene $1.5\times {10}^{-3}/{}^{\circ }\mathrm{C}$. The temperature at which a piece of this wood would just sink in benzene at the same temperature is

The length of a steel rod exceeds that of a brass rod by $5 \mathrm{cm}$. If the difference in their lengths remains same at all temperatures, then the length of brass rod will be: ($\alpha$ for iron and brass are $12\times {10}^{-6}/{}^{\circ }\mathrm{C}$ and $18\times {10}^{-6}/{}^{\circ }\mathrm{C}$, respectively)

The apparent coefficient of expansion of a liquid when heated, filled in vessel $A$ and $B$ of identical volumes, is found to be ${\gamma }_1$ and ${\gamma }_2$, respectively. If ${\alpha }_1$ be the linear expansivity of $A$ then that of $B$ will be

A glass vessel is filled up to 3/5th of its volume by mercury. If the volume expansivities of glass and mercury be 9 x 10^-6/^oC and 18 x 10^-5/^oC, respectively, then the coefficient of apparent expansion of mercury is