A body takes 10 min to cool douwn from `62^@C` to `50^@C`. If the temperature of surrounding is `26^@C` then in the next 10 minutes temperature of the body will be

Options

A. `38^(@)C`
B. `40^(@)C`
C. `42^(@)C`
D. `44^(@)C`

Answer

C

Explanation

From Newton.s colling law
`(theta_(1)-theta_(2))/(t)=K((theta_(1)+theta_(2))/(2)-26)`
Case I `12/(10)=Kxx30`
`K=12/(10xx30)=1/(25)`
Case : II `(50-theta_(2))/(10)=K((50+theta_(2))/(2)-26)`
`(50-theta_(2))/(10)=1/(25)((theta_(2)-2)/(2))`
`250-5theta_(2)=theta_(2)-2`
`6theta_(2)=252`
`theta_(2)=252/(6)=42^(@)C`