Assertion (A): For small temperature difference between body and surrounding, the rate of cooling directly proportional to the difference in temperature, known as Newton’s law of cooling.
Reason (R): Newton’s law of cooling is valid for heat transfer by radiation mode only.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) correctly states Newton's law of cooling. Reason (R) is false; Newton's law of cooling is primarily derived from convection, and it is a good approximation for small temperature differences involving conduction and convection, not exclusively radiation.
Assertion (A): For small temperature difference between body and surrounding, the rate of cooling directly proportional to the difference in temperature, known as Newton’s law of cooling.
Reason (R): Newton’s law of cooling is valid for heat transfer by radiation mode only.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is the correct statement of Newton's Law of Cooling. Reason (R) is false, as the law applies to convection and can be approximated from radiation for small temperature differences, not exclusively for radiation.
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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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.