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Hello students, in this question we are utilizing newton's law of cooling that is t minus t s is equal to t 0 minus t s into e raised to minus k into t.
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This is the equation for newton's law of cooling where t is the temperature at the instance, t s is the temperature of surrounding and t 0 is the initial temperature of the substance, t time and k is the constant.
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So, first it is given that at t is equal to 6 seconds temperature becomes 80 degree centigrade and after t is equal to 8 seconds, 2 more seconds temperature becomes 50 degree centigrade and the surrounding temperature is given as 20 degree centigrade.
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Applying these values in the equation we have 80 minus 20 is equal to t 0 minus 20 e raised to minus 6 k equation number 1 and 50 minus 20 which is equal to t 0 minus 20 e raised to minus 8 k equation number 2.
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So, rearranging equation 1 we have 60 is equal to t 0 minus 20 into e raised to minus 6 k or we can write e raised to minus 6 k is equal to 60 divided by t 0 minus 20 equation number 3.
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Similarly, e raised to minus 8 k can be written as 30 divided by t 0 minus 20.
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So, if we substitute e raised to minus 6 k here t 0 minus 20 so we have t 0 minus 20 will be equal to 60 divided by e raised to minus 6 k.
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So, substituting the value we have e raised to minus 8 k is equal to 30 divided by 60 into e raised to minus 6 k.
02:35
So, we have that is equal to e raised to minus 6 k by 60 will be equal to so rearranging that t 0 minus 20 can be equal to 30 divided by e raised to minus 8 k equation a...