Home
Class 12
PHYSICS
Water at 60^(@)C cools to 50^(@)C in the...

Water at `60^(@)C` cools to `50^(@)C` in the first 10 min and to `42^(@)C` in the next 10 min. the temperature of the surrounding is

A

`10^(@)C`

B

`15^(@)C`

C

`20^(@)C`

D

`25^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
A
By Newton.s law of cooling,
Rate of loss of heat=`Kxx`Mean difference in temperature
In first area, `(60-50)/(10)=K((60+50)/(2)-theta)`
`implies 1=K(55-theta)` . . . (i)
In second case, `(50-42)/(10)=K((50+42)/(2)-theta)`
`implies (8)/(10)=K(46-theta)` . . . (ii)
From eqs. (i) and (ii), `(8)/(10)=((46-theta))/((55-theta))implies (4)/(5)=((46-theta))/((55-theta)`
`implies 4(55-theta)=5(46-theta)`
`implies 220-48=230-5thetaimplies theta=10^(@)C`
Promotional Banner

Similar Questions

Explore conceptually related problems

Hot water cools from 60^@C to 50^@C in the first 10 min and to 42^@C in the next 10 min. The temperature of the surrounding is

Hot water cools from 60^(@)C to 50^(@)C in the first 10 minutes and to 45^(@)C in the next 10 minutes. The temperature of the surroundings is:

Certain quantity of water cools from 70^(@)C to 60^(@)C in the first 5 minutes and to 54^(@)C in the next 5 minutes. The temperature of the surrounding is

A body cools from 50^(@)C to 46^(@)C in 5 min and to 40^(@)C in the next 10 min. then the temperature of the surrounding is

A body initially at 80^(@)C cools to 64^(@)C in 5 minutes and to 52^(@)C in 10 minutes. What is the temperature of the surroundings?

A body cools from 70^(@)C" to "60^(@)C in 5 minutes and to 45^(@)C in the next 10 minutes. Calculate the temperature of the surroundings.

A body cools from 62 ^@ C to 54 ^@ C in 10 minutes and to 48^@ C in the next 10 minutes. Find the temperature of the surroundings.

A liquid cools from 50^(@)C to 45^(@)C in 5 minutes and from 45^(@)C to 41.5^(@)C in the next 5 minutes. The temperature of the surrounding is