The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha _1$ and $\alpha _2$. If the difference between the two lengths is independent of temperatures

Steam at $100\,^oC$ is passed into $22\,g$ of water at $20\,^oC$. The mass of water that will be present when the water acquires a temperature of $90\,^oC$ (Latent heat of steam is $540\, cal/g$ ) is ………… $\mathrm{g}$

If an electric heater is rated at $1000\,W$, then the time required to heat one litre of water from $20\,^oC$ to $60\,^oC$ is

A lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking is …….. $m/s$ ($M.P.$ of lead $= 327\,^oC,$ specific heat of lead $= 0.03\,cal/g\,^oC,$ latent heat of  fusion of lead $= 6\,cal/g$ and $J = 4.2\,joule/cal$ )

A faulty thermometer has its fixed points marked $5^o$ and $95^o$. This thermometer reads the temperature of a body as $59^o$. Then, the correct temperature of the body on the Celsius scale is …… $^o$