According to Newton’s law of cooling, the rate of change of temperature is proportional to the temperature difference between the system and its surroundings:dT/dt= -α(T-Tsur)where Tsur is the temperature of the surroundings and α is a constant. (a) Integrate this equation with the initial condition that T = Ti at t = 0.(b) Given that the entropy varies with temperature according to S(T) − S(Ti) = C ln(T/Ti), where Ti is the initial temperature and C the heat capacity, deduce an expression entropy of the system at time t.

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Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.