The temperature of a body on Kelvin scale is found to be $X\;K$. When it is measured by a Fahrenheit thermometer, it is found to be ${X^0}F$. Then $X$ is

Explain why :

$(a)$ a body with large reflectivity is a poor emitter

$(b)$ a brass tumbler feels much colder than a wooden tray on a chilly day

$(c)$ an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace

$(d)$ the earth without its atmosphere would be inhospitably cold

$(e)$ heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

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 $J = 4.2\,joule/cal$ )

Two substances $A$ and $B$ of equal mass $m$ are heated at uniform rate of $6\,cal\,s^{-1}$ under similar conditions. A graph between temperature and time is shown in figure. Ratio of heat absorbed $H_A/H_B$ by them for complete fusion is

A clock which keeps correct time at $20\,^oC$ has a pendulum rod made of brass. How many seconds will it gain or lose per day when temperature falls to $0\,^oC$ ? $(\alpha = 18\times10^{-6}/^oC)$

$200\, g$ of a solid ball at $20\,^oC$ is dropped in an equal amount of water at $80\,^oC$ . The resulting temperature is $60\,^oC$ . This means that specific heat of solid is