A solid copper sphere of density , specific heat capacity C and radius r is initially at 200 ~K . It is suspended inside a chamber whose walls are at 0 ~K . The time required (in s ) for the temperature of the sphere to drop to 100 ~K is ( is Stefan's constant and all the quantities are in SI units.)

Step-by-step solution

Here, T=200 ~K and T₀=0 ~K As the rate of fall of temperature, T t = A e (T^4-T₀^4 ) m s where, = Stefan's constant, A= area of sphere, and e= emissivity =1 and S= specific heat capacity. aligned & So, t= m s T A (T^4-T₀^4 ) & ( T₀=0 ~K ) & t= ( V) C(200 ~K -100 ~K ) (A) (200^4-0^4 ) & t= 4 3 r^3 C 100 4 r^2 (200)^4 & t= 1 48 r C 10⁻⁶ ~s = 1 48 r C s & aligned Hence, the correct option is (b).