An electric kettle (rated accurately at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\,^oC$ to boiling point. It takes $9.5$ minute. Then, the amount of heat that has been lost is

In an industrial process $10\, kg$ of water per hour is to be heated from $20^o C$ to $80^o C$ . To do this steam at $200^o C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^o C$. How many kg of steam is required per hour. (Specific heat of steam $= 0.5\, cal/g^o C$, Latent heat of vaporisation $= 540 cal/g)$

In the definition of 'calorie' one calorie is the heat required to raise the temperature of $1\  gram$ of water through $1\  ^oC$ in a certain interval of temperature. The temperature interval is

An aluminium container of mass $100\,\, gm$ contains $200 \,\,gm$ of ice at $-20^o\,\, C$. Heat is added to the system at the rate of $100 \,\,cal/s$. The temperature of the system after $4$ minutes will be ……. $^oC$ (specific heat of ice $= 0.5$ and $L = 80 \,\,cal/gm$, specific heat of $Al= 0.2\,\, cal/gm/^o C$)

$50 \,g$ ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \,g$ water at $30^{\circ} C$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is ………. $g$