The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha $, then coefficient of linear expansion of $B$
$\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$
$\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$
$\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $
If an electric heater is rated at $1000\,W$, then the time required to heat one litre of water from $20\,^oC$ to $60\,^oC$ is
The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha _1$ and $\alpha _2$ respectively. If the difference between the two length is independent of temperatures, then
$2\,kg$ of metal at $100\,^oC$ is cooled by $1\,kg$ of water at $0\,^oC$ . If specific heat capacity of metal is $\frac {1}{2}$ of specific heat capacity of water, final temperature of mixture would be
Steam at $100\,^oC$ is passed into $1.1\,kg$ of water contained in calorimeter of water equivalent $0.02\ kg$ at $15\,^oC$ till the temperature of the calorimeter rises to $80\,^oC$. The mass of steam condensed in kilogram is
$540\ g$ of ice at $0\ ^oC$ is mixed with $540\ g$ water at $80\ ^oC$. The final temperature of the mixture is