A geyser heats water flowing at a rate of $2.0 kg$ per minute from $30^{\circ} C$ to $70^{\circ} C$. If geyser operates on a gas burner, the rate of combustion of fuel will be $\dots \; g \min ^{-1}$
[Heat of combustion $=8 \times 10^{3} Jg ^{-1}$ Specific heat of water $=4.2 Jg ^{-1} \; { }^{\circ} C ^{-1}$ ]
$32$
$42$
$52$
$62$
A lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it, the initial speed of bullet is ............ $ms ^{-1}$
(Given, initial temperature of the bullet $=127^{\circ} C$,
Melting point of the bullet $=327^{\circ} C$,
Latent heat of fusion of lead $=2.5 \times 10^{4} \,J Kg ^{-1}$,
Specific heat capacity of lead $=125 \,J / kg K$ )
In an industrial process $10\, kg$ of water per hour is to be heated from $20°C$ to $80°C$. To do this steam at $150°C$ 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 $90°C.$ how many $kg$ of steam is required per hour. $($Specific heat of steam $= 1$ $calorie \,per\, gm°C,$ Latent heat of vaporisation $= 540 \,cal/gm)$
A liquid at $30^{\circ} C$ is poured very slowly into a Calorimeter that is at temperature of $110^{\circ} C$. The boiling temperature of the liquid is $80^{\circ} C$. It is found that the first $5 gm$ of the liquid completely evaporates. After pouring another $80 gm$ of the liquid the equilibrium temperature is found to be $50^{\circ} C$. The ratio of the Latent heat of the liquid to its specific heat will be. . . . .${ }^{\circ} C$. [Neglect the heat exchange with surrounding]
A calorimeter of water equivalent $20\, g$ contains $180\, g$ of water at $25^{\circ} C$. '$m$' grams of steam at $100^{\circ} C$ is mixed in it till the temperature of the mixure is $31^{\circ} C$. The value of $'m'$ is close to
(Latent heat of water $=540$ cal $g ^{-1}$, specific heat of water $=1$ cal $g^{-1}{ }^{\circ} C ^{-1}$ )
Steam at $100\,^oC$ is passed into $20\, g$ of water at $10\,^oC$. When water acquires a temperature of $80\,^oC$, the mass of water present will be ........ $g$
[Take specific heat of water $= 1\, cal\, g^{-1}\,^oC^{-1}$ and latent heat of steam $= 540\, cal\, g^{-1}$]