A small system of 1 mole has 3 degrees of freedom translatio

A small system of 1 mole has 3 degrees of freedom (translational) and 2 degrees of freedom (rotational) for each molecule. This system is in thermal equilibrium with a large reservoir. What is the total number of degrees of freedom? If the average thermal energy in the system is epsilon = 3200 J, what is the temperature of the large reservoir Find the range of energy Delta epsilon around epsilon, where 68% of the total energy is faind.

Solution

The reservoirs are large systems that provide equilibrium for the smaller system. Areservoir is a system with an extremely large number of degrees of freedom.

a] Total number of degrees of fredom= 3+2= 5

b] E= 3200J

E= 1/2kT* 5

3200= 5/2* 1.38*10^-23 T

T= 927.54*10²³K

c] delta E= 0.68*3200J= 2176 J

Range of energy= E- delta E= 3200-2176= 1024 J