A vessel contains $110\,\,g$  of water. The heat capacity of the vessel is equal to $10\,\,g$ of water. The initial temperature of water in vessel is $10\,^oC.$  If $220\,\,g$  of hot water at $70\,^oC$  is poured in the vessel, the final temperature neglecting radiation loss, will be nearly equal to ........ $^oC$

A continuous flow water heater (geyser) has an electrical power rating $= 2 \,\,kW$ and efficienty of conversion of electrical power into heat $ = 80 \%$. If water is flowing through the device at the rate of $100 \,\,cc/sec$, and the inlet temperature is $10^o C$, the outlet temperature will be ....... $^oC$ 

Two identical blocks of metal are at $20^{\circ} C$ and $80^{\circ} C$, respectively. The specific heat of the material of the two blocks increases with temperature. Which of the following is true about the final temperature $T_f$ when the two blocks are brought into contact (assuming that no heat is lost to the surroundings)?

When $0.93\,watt-hour$ of energy is supplied to a block of ice weighing $10\,g,$ it is found that

A 'thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side $30 \,cm$ has a thickness of $5.0\; cm .$ If $4.0\; kg$ of ice is put in the box, estimate the amount of ice (in $kg$) remaining after $6 \;h$. The outside temperature is $45\,^{\circ} C ,$ and co-efficient of thermal conductivity of thermacole is $0.01\; J s ^{-1} m ^{-1} K ^{-1} .$ Heat of fuston of water $=335 \times 10^{3}\;J kg ^{-1} $

A block of ice of mass $120\,g$ at temperature $0^{\circ} C$ is put in $300\,gm$ of water at $25^{\circ} C$. The $xg$ of ice melts as the temperature of the water reaches $0^{\circ} C$. The value of $x$ is

[Use: Specific heat capacity of water $=4200$

$J\,kg ^{-1} K ^{-1}$, Latent heat of ice $\left.=3.5 \times 10^{5} J\,kg ^{-1}\right]$