Question

47. Two bodies A and B of same mass, area and surface
finish with specific heats SA and SB (SA> SB) are
allowed to cool for given temperature range.
Temperature varies with time as

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Answer 1

Answer:

as we can see it inversely depends on the specific heat capacity

so slope of A will be smaller than slope of B

So option 1) is correct

Explanation:

As we know that rate of heat radiation to the surrounding is given as

$\frac{dQ}{dt} = \sigma A(\theta^4 - \theta_s^4)$

now we know that

$Q = ms(\theta)$

so we have

$\frac{dQ}{dt} = ms\frac{d\theta}{dt}$

now we have

$ms\frac{d\theta}{dt} = \sigma A(\theta^4 - \theta_s^4)$

so we have

$\frac{d\theta}{dt} = \frac{\sigma A}{ms}(\theta^4 - \theta_s^4)$

so we will have more slope for smaller heat capacity as we can see it inversely depends on the specific heat capacity

so slope of A will be smaller than slope of B

So option 1) is correct

#Learn

Topic : Rate of cooling and thermal radiation

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