Question

a metal ball is heated upto temperature of 100°Celsius and at t=0 it is placed in waster which is maintained at 40°Celsius if the. temperature is reduced to 60°Celsius in 4 minutes find the time at which temperature of the ball is 50°Celsius

Answer 1

Answer:

6.5 min

Step-by-step explanation:

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Answer 2

Concept:

As a measure of the typical translational kinetic energy per atom or molecule in the system, temperature is a physical measurement that indicates how hot matter is. Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given:

Here it is given that a metal ball is heated up to temperature of $100$°Celsius and at $t=0$ it is placed in waster which is maintained at $40$°Celsius if the. temperature is reduced to $60$°Celsius in $4$ minutes.

Find:

We have to find  at which temperature of the ball is $50$°Celsius.

Solution:

According to the question,

$dT/T-40=-k dt$

Integrating both sides,

$log(T-40)=-kt+C$

Now, using the condition we can say that

$log(T-40)=-kt+log(60)\\= > log(T-40/60)=-4k....(2)$

using condition $(2)$

$log\frac{20}{60} =-4k$

$k=1/4log(3)$

Now. the equation $(2)$ becomes

$log(T-40/60)=-t/4log3\\= > t/4log3=log60/T-40$

So, when $T=50$°C is ->

$t/4log 3=log6\\= > t=6.52$min.

Hence, the time required will be $6.52min$.

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