A body cools from $$70$$∘c to $$50$$∘c in $$6$$ minutes. If temperature of surroundings is $$30$$∘c. What is the temperature after $$12$$ minutes?

Question

A body cools from $$70$$∘c  to  $$50$$∘c in $$6$$ minutes. If temperature of surroundings is  $$30$$∘c.  What is the temperature after $$12$$ minutes?

Infinity Learn · Accepted Answer

initial temperature of the body is θ$$1=70oc$$  after $$6$$ minutestemperature of body is θ$$2=50oc$$; surrounding temperature is     θ$$0=30oc$$; final temperature of body is    θ $$=$$? time $$t1=6$$ minutestime $$t2=12$$ minutesfrom newton law of cooling  dθ$$dt=-k$$θ$$1+$$θ$$22-$$θ$$0---(1)$$  substitute given values in $$eqn(1)$$      θ$$1-$$θ$$2time=-k$$θ$$1+$$θ$$22-$$θ$$070-506=-k70+502-30206=-k60-30k=-19---(2)$$  substitute second part of question, given values and $$eqn(2)$$ in $$eqn(1)50-$$θ$$12=--1950+$$θ$$2-30$$ ⇒θ$$=340C$$

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