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A pan filled with hot food cools from 94...

A pan filled with hot food cools from `94^(@)C` to `86^(@)C` in 2 minutes when th room temperature is at `20^(@)C`. How long will it take to cook from `71^(@)C` to `69^(@)C` ?

Text Solution

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According to Newton.s law of cooling,
`-(dT)/(dt)=K(T-T_(S))`
`-(86-94)/(120)=K[(94+86)/(2)-20]`
where `T=(94+86)/(2)=90^(@)C`
`T_(S)=` room temperature `=20^(@)C`
`(8)/(120)=k(70)`
`:.K=(8)/(120xx70)`
Now, again, `-(dT.)/(t)=K(T.-T_(S))`
`:.-(69-71)/(t)=(8)/(120xx70)[(71+69)/(2)-20]`
`:.2/t=(8)/(120xx70)xx(70-20)`
`:.2/t=(8xx50)/(120xx70)`
`:.t=(2xx120xx70)/(8xx50)`
`:.t=42s`
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