Heat and Thermal ExpansionHard
Question
A spherical body with an initial temperature T1 is allowed to coll in surrounding at temperature T0(< T1). The mass of the body is m. its gram spcific heat is c ,density ρ area A . If σ be the Stefan′S constant then the temperature T of the body the at time t can best represented by : -
Options
A.T = (T1 - T0) e-kt where k = 
B.T = (T1 - T0) ln (kt) where k = 
C.T = T0 + (T1 - T0) e-kt where k = 
D.T = T1 e-kt - T where k = 
Solution
From newton′s law of cooling.
σA (T4 - T04) = ms
⇒ σ.4r2 [(T0 + ᐃT)4) - T04] ρ
πr3c
⇒
(T - T0) = - 
⇒ K (T - T0) dt = - dT ⇒ k
⇒ T = T0 + (T1 - T0) e-kt where K =
σA (T4 - T04) = ms
⇒ σ.4r2 [(T0 + ᐃT)4) - T04] ρ
πr3c ⇒
(T - T0) = - ⇒ K (T - T0) dt = - dT ⇒ k
⇒ T = T0 + (T1 - T0) e-kt where K =
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