# A cup of coffee cools from 90° C to 80° C in t minutes, when the room temperature is 20° C. The time taken by a similar cup of coffee to cool from 80° C to 60° C at a room temperature same at 20° C is - a. 5/13 t b. 13/10 t c. 13/5 t d. 10/13 t

By Shivank Goel|Updated : August 10th, 2022

The rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings Newton's law of cooling.

From Newton’s law of cooling,

T1 - T2/ t = α (T1 + T2/ 2 - T0)

In the first case,

(90 - 80)/ t = α (90 + 80/2 - 20) .... (1)

In the second case,

(80 - 60)/t' = α (80 + 60/ 2 - 20) .... (2)

By solving both the equations

t' = 13t/5

Therefore, the time taken for a similar cup of coffee to cool from 80° C to 60° C at room temperature the same at 20° C is 13t/5.

Summary:

4. ## 10/13 t

A cup of coffee cools from 90° C to 80° C in t minutes, when the room temperature is 20° C. The time taken by a similar cup of coffee to cool from 80° C to 60° C at room temperature the same at 20° C is 13t/5.

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