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Question
A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45°C if the temperature of surroundings is 25°C.
Solution
Given that for the metal sphere
`((d theta)/dt)_1=4^@`C/min,
`theta_1=50^@C, theta_2=45^@ and theta_0=25^C`
By Newton's law of cooling,
`((d theta)/dt)=k(theta-theta_0)`
`therefore((d theta)/dt)_1/((d theta)/dt)_2=((theta_1-theta_0))/((theta_2-theta_0)`
`therefore((d theta)/dt)_1/((d theta)/dt)_2=((50^@-25^0))/((45^@-25^@)`
`therefore ((d theta)/dt)_2=20^@/25^@*((d theta)/dt)_1=20^@/25^@*4=3.2`
`therefore ((d theta)/dt)_2=3.2^@`C/min
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