Question

if temperature of a system decreases from 60c to 50c in 10 mins and then 50c to 42c in next 10min.what is the temperature of surrounding.

Answer 1

Do you know how to set up the equation for Heat lost = Heat gained?

Answer 2

\[q = m.s.\Delta t\]

Answer 3

If we assume that the system cools down exponentially (this is usually a good model), the formula for temperature T after time t is:
\[T=A*e^{-Bt}+C\]
Now, we know three points from the curve (= three unknowns, three equations) and therefore we can calculate all the coefficients A, B and C:
When t=0, then T=60
When t=10, then T=50
When t=20, then T=42.

By substituting the values, we get a set of equations:
\[60=A*e^{-B\cdot 0}+C\]
\[50=A*e^{-B\cdot 10}+C\]
\[42=A*e^{-B\cdot 20}+C\]
From which we can solve C=10. This is the final solution for the problem, because when t approaches infinity, the exponential term will go to zero and C will be the final temperature. So the answer is 10 celcius.