A thermos flask consists of two thin-walled coaxial cylinders with a narrow gap such that the radius ratio R 1 /R 2 = 0.95. The surfaces that face each other are silvered and have emissivity of 0.05...

A thermos flask consists of two thin-walled coaxial cylinders with a narrow gap such that the radius ratio R₁/R₂
= 0.95. The surfaces that face each other are silvered and have emissivity of 0.05 each. The annulus is evacuated. The length of flask is L = 0.3 m and the radius R₁
= 0.05 m. Calculate the heat loss when the thermos flask is filled with hot water such that T₁
= 373 K while the outer cylinder at a temperature of T₂
= 300 K. Also calculate the instantaneous rate of change of temperature of hot water.

Hints: Eq. (7.69) is used to find

Initial cooling rate of hot water at 100ºC is obtained by finding the properties of water at 373 K like
 and c_p. Then mass of water in the flask m =
 kg and the rate of cooling is