NEET Physics Question - Thermal Physics

Assertion (A): A hot body is kept in surrounding. As it cools, its temperature falls from \(80^0 C\) to \(78^0 C\) in a time duration \(t_1\) and from \(50^0 C\) to \(48^0 C\) in time duration \(t_2\). The temperature of surrounding is constant \(20^0 C\), then \(t_1 > t_2\).

Reason (R): According to Newton's law of cooling, rate of cooling depends only on the difference of temperature of the body and the surrounding.

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

Newton's law of cooling states that the rate of cooling `\(\frac{dT}{dt}\) ` is proportional to `\((T - T_s)\)`. For the first interval, average `\(T_{avg1} = 79^0 C\) ⇒ \(T_{avg1} - T_s) = 59^0 C\)`. For the second interval, average `\(T_{avg2} = 49^0 C\) ⇒ (T_{avg2} - T_s) = 29^0 C\)`. Since the temperature difference is greater in the first case, the rate of cooling is faster, meaning `\(t_1 < t_2\)`. So, Assertion (A) is false. Reason (R) states 'depends *only* on the difference', which is misleading as the rate also depends on factors like surface area and emissivity, embedded in the constant of proportionality. Thus, Reason (R) is also false under strict interpretation.

Rankers Physics

Newton’s Law of Cooling

Solution:

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