Question

The thermal capacities of two bodies are in the ratio
of 1:4. If the rate of loss of heat are equal for the
two bodies under identical conditions of
surroundings, then the ratio of rate of fall of
temperature of the two bodies is -
(1) 1:4
(2) 4:1
(3) 1:8
(4) 8:1​

Answer 1

Answer:

(2) 4:1

Explanation:

By using average formula of newtons law of cooling ... if we equate Ti-Tf/dt for both we'll get the ans

Answer 2

The the ratio of rate of fall of  temperature (rate of coiling) of the two bodies is 4:1.

Explanation:

The rate of heat transfer is

$\frac{dQ}{dt} =ms\frac{dT}{dt}$

Here, $\frac{dT}{dt}$ is the rate of coiling and ms is the thermal capacity.

As  the rate of loss of heat are equal for the  two bodies under identical conditions of  surroundings, then

$(\frac{dQ}{dt})_{1} =(\frac{dQ}{dt})_{2}$

Also given the ratio of thermal capacities is 4:1.

so,

$1\times(\frac{dT}{dt})_1=4\times(\frac{dT}{dt})_2$

or,

$\frac{(\frac{dT}{dt})_1}{(\frac{dT}{dt})_2} =\frac{4}{1}$

Thus, the the ratio of rate of fall of  temperature (rate of coiling) of the two bodies is 4:1.

#Learn More: rate of heat loss.

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