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

- A
$13.5\ ^oC\,\,\, to\,\,\, 14.5\ ^oC$

- B
$6.5\ ^oC\,\,\, to\,\,\, 7.5\ ^oC$

- C
$14.5\ ^oC\,\,\, to\,\,\, 15.5\ ^oC$

- D
$98.5\ ^oC\,\,\, to\,\,\, 99.5\ ^oC$

A steam engine intakes $50\, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If latent heat of vaporization of steam is $540 \,cal g ^{-1}$, then the heat rejected by the steam engine per minute is .........$\times 10^{3}$$cal.$

- [JEE MAIN 2022]

A piece of ice (heat capacity $=$ $2100$ $J kg^{-1}$ $^o C^{-1}$ and latent heat $=$ $3.36$ $×$ $10^5$ $J kg^{-1}$) of mass $m$ grams is at $-5^o C$ at atmospheric pressure. It is given $420$ $J$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1$ $gm$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is ...... $gm$

The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal ^{-1}{ }^{\circ} C ^{-1}$ ), is ......... $g$

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

$20\, gm$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1\, cal/gm-\,^oC$) of mass $100\, gm$. The resulting temperature is ........ $^oC$