In: Physics
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.
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.