$A$ liquid of mass $m$ and specific heat $c$ is at a temperature of $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is at a temperature of $T$. What will be the final temperature of the mixture?

$A$ $210 \,W$ heater is used to heat $100 \,g$ of water. The time required to raise the temperature of this water from $25^{\circ} C$ to $100^{\circ} C$ is (specific heat capacity of water $= 4200 \,J / kg \cdot ^{\circ} C$). (in $\,s$)

$A$ beaker contains $200\,g$ of water. The heat capacity of the beaker is equal to that of $20\,g$ of water. The initial temperature of water in the beaker is $20\,^{\circ}C$. If $440\,g$ of hot water at $92\,^{\circ}C$ is poured in it,the final temperature (neglecting radiation loss) will be nearest to ........ $^{\circ}C$.

$0.1 \, m^3$ of water at $80 \, ^oC$ is mixed with $0.3 \, m^3$ of water at $60 \, ^oC$. The final temperature of the mixture is ........ $^oC$.

Steam at $100^{\circ}C$ is added slowly to $1400 \, \text{g}$ of water at $16^{\circ}C$ until the temperature of the water is raised to $80^{\circ}C$. The mass of steam required to do this is $(L_V = 540 \, \text{cal/g})$ ........... $\text{g}$

Water of volume $2\, L$ in a closed container is heated with a coil of $1\, kW$. While water is heated,the container loses energy at a rate of $160\, J/s$. In how much time will the temperature of water rise from $27\, ^\circ C$ to $77\, ^\circ C$? (Specific heat of water is $4.2\, kJ/kg\cdot K$ and that of the container is negligible)