$A$ geyser heats water flowing at the rate of $3.0 \, L/min$ from $27 \, ^{\circ}C$ to $77 \, ^{\circ}C$. If the geyser operates on a gas burner,what is the rate of consumption (in $g/min$) of the fuel if its heat of combustion is $4.0 \times 10^{4} \, J/g$?

$250\,g$ of water and an equal volume of alcohol of mass $200\,g$ are placed successively in the same calorimeter and cool from $60^{\circ}C$ to $55^{\circ}C$ in $130\,s$ and $67\,s$ respectively. If the water equivalent of the calorimeter is $10\,g$,then the specific heat of alcohol in $\text{cal/g}^{\circ}C$ is:

Water falls from a height of $500\,m$. The rise in temperature of the water at the bottom,assuming all energy remains in the water,will be ........ $^oC$ [Specific heat of water = $4.2\,kJ/kg\cdot K$]

Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$. The specific heat of ice is $2222.3\,J\,kg^{-1\circ}C^{-1}$ and the latent heat of fusion of ice is $336\,kJ\,kg^{-1}$.
$(A)$ Final temperature of the system will be $0^{\circ}C$.
$(B)$ Final temperature of the system will be greater than $0^{\circ}C$.
$(C)$ The final system will have a mixture of ice and water in the ratio of $5:1$.
$(D)$ The final system will have a mixture of ice and water in the ratio of $1:5$.
$(E)$ The final system will have water only.
Choose the correct answer from the options given below:

$A$ 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:

If in the winter season the surface temperature of a lake is $1^{\circ} C$,the temperature at the bottom of the lake will be ............