Question

A body takes T minutes to cool from 62⁰C to 61⁰C when the surrounding temperature is 30⁰C. The time taken by the body to cool from 46⁰C to 45.5⁰C is

• A. Greater than T minutes
• B. Equal to T minutes
• C. Less than T minutes
• D. Equal to T/2 minutes

Answer 1

Answer: (B)

Equal to T minutes

Answer 2

According to Newton's law of cooling

$\frac{\theta_{1} - \theta_{2}}{t} \propto \left\lbrack \frac{\theta_{1} + \theta_{2}}{2} - \theta \right\rbrack$

For first condition $\frac{62 - 61}{T} \propto \left\lbrack \frac{62 + 61}{2} - 30 \right\rbrack$ …..(i)

and for second condition $\frac{46 - 45.5}{t} \propto \left\lbrack \frac{46 + 45.5}{2} - 30 \right\rbrack$ .(ii)

By solving (i) and (ii) we get t = T sec.