1.

A pan filled with hot food cools form 94^(@)C to 86^(@)C in 2 minutes . When the roo temperature is 20^(@)C. How long will it cool from 74^(@)C to 66^(@)C ?

Answer»

2 MINUTES
2.8 minutes
2.5 minutes
1.8 minutes

Solution :From Newton.s law of cooling, `(d theta)/(dt)prop(theta-theta_(0))`
In Case (i), `(94-86)/(2)prop((94+86)/(2)-20)`
`IMPLIES (8)/(2)prop(90-20)`
or `4prop70""….(1)`
In Case (ii), `(74-66)/(t)prop((74+66)/(2)-20)`
`(8)/(t)prop(70-20)`
`(8)/(t)prop50""....(2)`
Dividing (1) and (2)
`(t)/(2)=(70)/(50)`
`t=(14)/(5)`
`t=2.8` minutes


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