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 $= 540 \,cal/gm)$
$1 \,gm$
$1\, kg$
$10\, gm$
$10 \,kg$
A drilling machine of $10\,KW$ power is used to drill a bore in a small aluminium block of mass $8\,kg.$ If $50\%$ of power is used up in heating the machine itself or lost to the surroundings then ........ $^oC$ is the rise in temperature of the block in $2.5\,minutes$
[specific heat of aluminium $= 0.91\,J/g\,\,^oc$ ]
One end of a $2.35\,\,m$ long and $2.0\,\,cm$ radius aluminium rod$(K = 235 \,\,W.m^{-1}K^{-1})$ is held at $20^0\,\,C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg.s^{-1}$ at which ice melts is
[Take latent heat of fusion for ice as $\frac{{10}}{3} ×10^5 J.kg^{-1} $]
A water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure), tr e wat'r from the cooler is used to cool an external device that generates constantly $3 \mathrm{~kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ} \mathrm{C}$ and the e.tire stored $120$ litres of water is initially cooled to $10^{\circ} \mathrm{C}$. The entire system is thermally insulat $\mathrm{d}$. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is
(Specific heat of water is $4.2 \mathrm{~kJ}^{-1} \mathrm{~kg}^{-1}$ and the density of water is $10.$) $0 \mathrm{k}^2 \mathrm{~m}^{-3}$ )
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 $=125 \,J / kg K$ )
$200 \,g$ of ice at $-20^{\circ} C$ is mixed with $500 \,g$ of water at $20^{\circ} C$ in an insulating vessel. Final mass of water in vessel is ........... $g$ (specific heat of ice $=0.5 \,cal g ^{-10} C ^{-1}$ )