Question

Give your interpretation of Newton’s law of cooling for internal flows:

a) Temperature increases linearly with time
b) Temperature decreases exponentially with time
c) Temperature remains constant
d) Temperature varies quadratically with time

Answer 1

Newton's law of cooling states that the rate of heat transfer between an object and its surroundings is directly proportional to the temperature difference between them. In the context of internal flows, such as the flow of fluids within a pipe or channel, Newton's law of cooling can be interpreted as follows:

b) Temperature decreases exponentially with time.

In internal flows, the temperature of the fluid tends to approach the temperature of the surrounding environment due to heat transfer. As the fluid flows through the system, it loses heat to the surroundings, causing its temperature to decrease. This heat transfer process follows an exponential decay pattern, where the temperature change is proportional to the temperature difference between the fluid and the surroundings.

Therefore, the correct interpretation of Newton's law of cooling for internal flows is that the temperature decreases exponentially with time.

Answer 2

Newton's law of cooling describes that theb. temperature of a body in an internal flow decreases exponentially with time relative to its surroundings.

Step-by-step explanation:

Newton's law of cooling for internal flows often describes the rate at which temperature changes within a fluid that is moving. Newton's law of cooling suggests that the temperature of a body changes at a rate proportional to the difference between its own temperature and the ambient temperature, i.e., the temperature decreases exponentially with time when it is hotter than the surroundings. When the body is cooler, the reverse process occurs, and the body warms up towards the ambient temperature, again following an exponential approach.

The internal energy of a gas can also change according to its interactions with its surroundings. When a gas rapidly expands, as per the first law of thermodynamics, it does work on its surroundings, leading to a decrease in its internal energy, hence the temperature of the gas decreases. This rate of change in the temperature is contingent on factors like heat transfer through conduction, the gas's specific heat, and the nature of the expansion.