Newton’s law of cooling states that the rate of cooling of a body is proportional to the _____________________.a)temperature of the surroundingsb)excess temperature of the body over the surroundingsc)temperature of the bodyd)temperature of the body + temperature of the surroundingsCorrect answer is option 'B'. Can you explain this answer?

Question

Newton&#8217;s law of cooling states that the rate of cooling of a body is proportional to the _____________________.a)temperature of the surroundingsb)excess temperature of the body over the surroundingsc)temperature of the bodyd)temperature of the body + temperature of the surroundingsCorrect answer is option 'B'. Can you explain this answer?

Answer

Newton's law of cooling states that the heat released by a body with respect to time (or) the rate of heat released is directly proportional to the difference between the body's temperature and the surrounding temperature.

dH/dt = k(T - t) where t = surrounding's temperature and T = temperature of the body

Consider two bodies A and B, of equal surface areas, such that A's temperature is more that B's temperature and the surrounding temperature is less than both A and B. Then according to Newton's law of cooling A looses more heat to the surroundings when compared B during the same time interval. So, A will cool more faster than B.

Answer

Newton's law
dq/dt directly proportional to difference in tempatature of the body and temparature of soroundings

Answer

Newton's Law of Cooling states that the rate of cooling of a body is proportional to the excess temperature of the body over the surroundings. In other words, the rate at which an object cools down is directly related to the temperature difference between the object and its surroundings.

Explanation:

Rate of Cooling:
The rate of cooling refers to how quickly an object loses heat or decreases in temperature. It is influenced by factors such as the surface area of the object, the nature of the surface, and the temperature difference between the object and its surroundings.

Excess Temperature:
The excess temperature of a body over the surroundings is the difference between the temperature of the body and the temperature of the surroundings. If the body is at a higher temperature than its surroundings, there will be a temperature difference, resulting in heat transfer from the body to the surroundings.

Proportional Relationship:
According to Newton's Law of Cooling, the rate of cooling is directly proportional to the excess temperature. This means that as the excess temperature increases, the rate of cooling also increases, and vice versa. Mathematically, this relationship can be expressed as:

Rate of Cooling ∝ Excess Temperature

This proportionality constant can be represented as the cooling constant (k). Therefore, we can rewrite the relationship as:

Rate of Cooling = k * Excess Temperature

The cooling constant (k) depends on various factors such as the nature of the object's surface, the surrounding medium, and the conditions under which the cooling occurs. It can be determined experimentally for specific objects and environments.

Significance:
Newton's Law of Cooling is applicable to a wide range of scenarios where heat transfer occurs between an object and its surroundings. It helps us understand how objects cool down and how the cooling rate can be influenced by different factors. This law is often used in practical applications, such as in the design of cooling systems, weather forecasting, and understanding the behavior of various materials at different temperatures.

In summary, Newton's Law of Cooling states that the rate of cooling of a body is proportional to the excess temperature of the body over the surroundings. This relationship helps us explain and predict the cooling behavior of objects in various environments.

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