Question

A hot liquid is filled in a container and kept in a room of temperature of 25${}^{\circ }$C. The liquid emits heat at the rate of 200 Js${}^{-1}$ when its temperature is 75${}^{\circ }$C. When the temperature of the liquid becomes 40${}^{\circ }$C, the rate of heat loss is J s${}^{-1}$ is

• A. 160
• B. 140
• C. 80
• D. 60
• E. 40

Answer 1

Answer: (D)

Rate of cooling $\left(\frac{-d\theta }{dt}\right)=\alpha (\theta -{\theta }_0)$
$or\frac{(\frac{-d\theta }{dt}{)}_1}{(\frac{-d\theta }{dt}{)}_2}=\frac{{\theta }_1-{\theta }_0}{{\theta }_2-{\theta }_0}$
$or\frac{200}{(\frac{-d\theta }{dt}{)}_2}=\frac{75-25}{40-25}$
$or(-\frac{d\theta }{dt}{)}_2=\frac{15}{20}\times 200=60J{s}^{-1}$