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A body cools in a surrounding of constan...

A body cools in a surrounding of constant temperature `30^@C` Its heat capacity is `2 J//^(@)C`. Initial temeprature of cooling is valid. The body cools to `38^@C` in 10 min
In further 10 min it will cools from `38^@C` to _____

A

`36^@C`

B

`36.4^@C`

C

`37^@C`

D

`37.5^@C`

Text Solution

Verified by Experts

The correct Answer is:
B
We have `theta-theta_s=(theta_0-theta_s)e^(-kt)`
Where `theta_0=`initial temperature of body `=40^@C`
`theta=`temperature of body after time t.
Since body cools from 40 to 38 in 10 min, we have
`38-30=(40-30)e^(-10k)` .(i)
Let after 10 min, the body temperature be `theta`
`theta-30^@=(38-30)e^(-10k)` .(ii)
`(Eq(i))/(Eq(ii))`gives `(8)/(theta-30)=(10)/(8)`,`theta-30=6.4`
`theta=36.4^@C`
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Knowledge Check

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