26/04/19 If two metal blocks of initially different temperatures come together and equilibrate to the same...

26/04/19

If two metal blocks of initially different temperatures come together and equilibrate to the same temperature and produce a total change in entropy of 6.2 JK^-1, what is the factor by which the number of microstates in the universe increases? Is this done using Boltzmann entropy?

Also, please explain what the second law of thermodynamics is statistically based on.

Solutions

Expert Solution

In statistical mechanics, the equation relating entropy with number of microstates is Boltzman Entropy equation given by.

Now since the entropy of universe always increase, the change in entropy given is positive.

To calculate the increase in number of microstates, we reshuffle the above equation to get . Here is Boltzman constant. Since a small system has large number of microstates, so for an entropy change of 6.2, the microstates becomes infinite.

Second law of thermodynamics is based on the direction of evolution of a process. Kelvin Planck's statement says there is no system, which converts all the given heat completely into work, which suggest statistically that, entropy of a system never decreases and therefore number of microstates of a system always increases.

For example- Consider an isolated system, in which there are two boxes at different temperatures T1 and T2 (T1 > T2). Now the system will try to come in equilibrium by equalizing the temperatures. Now suppose Q be the heat transferred between the boxes. So change in entropy of the system will be and since T1>T2, so entropy change will be positive and therefore entropy of the universe always increases.

genius_generous answered 1 year ago

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