Question

Hot water cools from 60^0C to 50^0C in the first 10 minutes and to 42^0C in the next 10 minutes. The temperature of the surrounding

• A. 5^0C
• B. 10^0C
• C. 15^0C
• D. 20^0C

Answer 1

Answer: (B)

10^0C

Answer 2

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

For first condition $\frac{60 - 50}{10} \propto \left\lbrack \frac{60 + 50}{2} - \theta \right\rbrack$

⇒ 1 = K [55 – θ] ……(i)

For second condition $\frac{50 - 42}{10} \propto \left\lbrack \frac{50 + 42}{2} - \theta \right\rbrack$

⇒ 0.8 = K (46 – θ ) …..(ii)

From (i) and (ii) we get θ = 10^oC