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 $=125 \,J / kg K$ )

Ice at $0^o C$ is added to $200 \,\,g$ of water initially at $70^o C$ in a vacuum flask. When $50\,\, g$ of ice has been added and has all melted the temperature of the flask and contents is $40^o C$. When a further $80\,\,g$ of ice has been added and has all metled, the temperature of the whole is $10^o C$. Calculate the specific latent heat of fusion of ice.[Take $S_w =1\,\, cal /gm ^o C$.]

Calorimeters are made of which of the following

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 liquid of mass $M$ and specific heat $S$ is at a temperature $2t$. If another liquid of thermal capacity $1.5$ times, at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be