Solveeit Logo
Login

Question

Question: If a metallic sphere gets cooled from \(62 ^ { \circ } \mathrm { C }\) to \(42 ^ { \circ } \mathrm...

If a metallic sphere gets cooled from 62∘C62 ^ { \circ } \mathrm { C } to 42∘C42 ^ { \circ } \mathrm { C }, then the temperature of the surroundings is

A

30∘C30 ^ { \circ } \mathrm { C }

B

36∘C36 ^ { \circ } \mathrm { C }

C

D

Answer

Explanation

Solution

θ1−θ2t=K[θ1+θ22−θ0]\frac { \theta _ { 1 } - \theta _ { 2 } } { t } = K \left[ \frac { \theta _ { 1 } + \theta _ { 2 } } { 2 } - \theta _ { 0 } \right]

In the first 10 minute

62−5010=K[62+502−θ0]\frac { 62 - 50 } { 10 } = K \left[ \frac { 62 + 50 } { 2 } - \theta _ { 0 } \right]⇒ 1.2=K[56−θ0]1.2 = K \left[ 56 - \theta _ { 0 } \right] .... (i)

Next 10 minute

0.8=K[46−θ0]0.8 = K \left[ 46 - \theta _ { 0 } \right] .... (ii)

from equations (i) and (ii) θ0=26∘C\theta _ { 0 } = 26 ^ { \circ } \mathrm { C }