When 100 J of heat is added to a system, resulting in a final temperature of 400 K, what is the change in entropy of the system? a) 0.25 J/K b) 2.5 J/K c) 1 J/K d) 4 J/K

To calculate the change in entropy (\( \Delta S \)) for a system when heat is added, we can use the formula for entropy change when heat is added or removed at a constant temperature:

\[ \Delta S = \frac{Q}{T} \]

where \( Q \) is the heat added to the system, and \( T \) is the final temperature of the system in Kelvin.

Given that \( Q = 100 \, J \) and \( T = 400 \, K \), we can plug these values into the formula:

\[ \Delta S = \frac{100 \, J}{400 \, K} = 0.25 \, J/K \]

So, the change in entropy of the system is \( 0.25 \, J/K \), which is option a).

Extra: Entropy is a measure of the disorder or randomness in a system. It's a central concept in the second law of thermodynamics, which essentially states that the total entropy of an isolated system can never decrease over time. In other words, natural processes tend to move towards a state of increased entropy.

In the context of heat transfer, when heat is added to a system at a constant temperature, the system's entropy increases. This is because heat energy increases the energy levels of the particles in the system, causing them to move more randomly and thus increasing disorder.

The unit of entropy is Joules per Kelvin (J/K), which gives an indication of how much the disorder or randomness of the system increases per unit of temperature for the heat energy added. The larger the entropy change for a given amount of heat, the bigger the increase in disorder. Entropy can be thought of as a measure of energy dispersal at a particular temperature.