# A thermos flask consists of two thin-walled coaxial cylinders with a narrow gap such that the radius

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 each. The annulus is evacuated. The length of flask is L = 0.3 m and the

radius R_{1} = 0.05 m. Calculate the heat loss when the thermos flask

is filled with hot water such that T_{1} = 373 K while the outer

cylinder at a temperature of T_{2} = 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