Question

If a metallic sphere gets cooled from ${62}^{\circ }C$ to ${50}^{\circ }C$ in 10 minutes and in the next 10 minutes gets cooled to ${42}^{\circ }C$, then the temperature of the surroundings is

• A. 30°C
• B. 36°C
• C. 26°C
• D. 20°C

Answer 1

The correct option is C

26°C

$\frac{{\theta }_1-{\theta }_2}{t}=K[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0]$

In the first 10 minute

$\frac{62-50}{10}=K[\frac{60+50}{2}-{\theta }_0]\Rightarrow 1.2=k[56-{\theta }_0]$ ...... (i)

$\frac{50-42}{10}=K[\frac{50+42}{2}-{\theta }_0]\Rightarrow 0.8=k[46-{\theta }_0]$ ...... (ii)

From equationd (i) and (ii) $\frac{1.2}{0.8}=\frac{(56-{\theta }_0)}{(46-{\theta }_0)}\Rightarrow {\theta }_0={26}^{\circ }C$