1. Tardigrade
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  3. Physics
  4. A hot liquid is filled in a container and kept in a room of temperature of 25°C. The liquid emits heat at the rate of 200 Js-1 when its temperature is 75°C. When the temperature of the liquid becomes 40°C, the rate of heat loss is J s-1 is

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Q. 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

KEAMKEAM 2008Thermal Properties of Matter

Solution:

Rate of cooling $ \bigg(\frac{-d\theta}{dt}\bigg)=\alpha (\theta-\theta_0)$
$or \, \, \, \, \, \, \, \, \, \, \, \frac{\bigg(\frac{-d\theta}{dt}\bigg)_1}{\bigg(\frac{-d\theta}{dt}\bigg)_2}=\frac{\theta_1 -\theta_0}{\theta_2 -\theta_0}$
$or \, \, \, \, \, \, \, \, \, \, \, \frac{200}{\bigg(\frac{-d\theta}{dt}\bigg)_2} =\frac{75-25}{40-25}$
$or \, \, \, \, \, \, \, \bigg(-\frac{d\theta}{dt}\bigg)_2 =\frac{15}{20} \times 200 =60Js^{-1}$