Q. 105.0( 1 Vote )

# A body cools down from 65°C to 60°C in 5 minutes. It will cool down from 60°C to 55°C in

A. 5 minutes

B. less than 5 minutes

C. more than 5 minutes

D. less than or more than 5 minutes depending on whether its mass is more than or less than 1 kg.

Answer :

According to Newton’s Law of Cooling:

Here is the rate of fall of temperature is the constant depending on nature of surface and surrounding conditions, A is the area of cross-section of the body, T is the average Temperature of the body and T_{0} is the surrounding temperature.

It can also be written in Celsius scale as

Where θ and θ_{0} are the temperature of the body and surrounding in Celsius scale respectively , k is a constant.

First condition:

Temperature falls from 65° C to 60° C.

Which means 5°C falls in 5 minutes,

∴

θ = 62.5 ° C

Substituting we get,

Second Condition:

Temperature further falls from 60 °C to 55 °C.

∴ dθ= 5 °C.

θ =

Substituting value of -k,dθ and θ in the equation we get,

Here we can conclude that time required for the body to go from 60 ° C to 55° C will be,

Thus, option (c) is the correct option.

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