Question 704: Thermodynamics & KTG

Question

A body cools from $60^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is $10^{\circ} \mathrm{C}$ )

Accepted Answer

According to Newton's law of cooling,
$$ \frac{	heta_1-	heta_2}{\mathrm{t}}=\mathrm{K}\left[\frac{	heta_1+	heta_2}{2}-	heta_0ight] $$
where, $	heta_0=$ temperature of surrounding
$$ \begin{aligned} 	herefore \quad & \frac{60-40}{6}=K\left[\frac{60+40}{2}-10ight] \ & \frac{20}{6}=K 	imes 40 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)\ & K=\frac{1}{12} \end{aligned} $$
After another t min , let the temperature be x .
$$ \begin{array}{ll} 	herefore & \frac{40-x}{6}=\frac{1}{12}\left[\frac{40+x}{2}-10ight] 	ext { ...[using (i)] }\ 	herefore & 40-x=\frac{20+x}{4} \ 	herefore & 160-4 x=20+x \ 	herefore & 5 x=140 \ 	herefore & x=\frac{140}{5}=28^{\circ} \mathrm{C} \end{array} $$

Answer

$24^{\circ} \mathrm{C}$

Answer

$28^{\circ} \mathrm{C}$

Answer

$18^{\circ} \mathrm{C}$

Answer

$32^{\circ} \mathrm{C}$

Thermodynamics & KTG

A body cools from 60^{\circ} \mathrm{C} to 40^{\circ} \mathrm{C} in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10^{\circ} \mathrm{C} )

Choose the correct answer: