A black body of mass `34.38` g and surface area `19.2cm^(2)` is at an intial temperature of 400 K. It is allowed to cool inside an evacuated enclosure kept at constant temperature 300 K. The rate of cooling is `0.04^(@)C//s`. The sepcific heat of the body `J kg^(-1)K^(-1)` is
(Stefan's constant, `sigma = 5.73 xx 10^(-8)Wm^(-2)K^(-4))`

Options

A. 2800
B. 2100
C. 1400
D. 1200

Answer

C

Explanation

Rate of cooling, `(d theta)/(dt)= (sigmaA(T^(4)-T_(s)^(4)))/(mS)`
Specific heats,
`S =(sigmaA(T^(4)-T_(s)^(4)))/(m)((dt)/(d theta))`
`= (5.73xx10^(-8)xx19.2xx10^(-4)(400^(4)-300)^(4))/(34.38xx10^(-3))((1)/(0.04))(because(d theta)/(dt)=0.04)`
`= 1400 Jkg^(-1)K^(-1)`