# Question & Answer: 2. Sketch System A according to the following criteria: System A has energy levels spaced 4 aJ…..

2. Sketch System A according to the following criteria: System A has energy levels spaced 4 aJ apart with a ground state of 0 aJ (Recall that 1 aJ = 1 times 10^-18 J). In this system, 8 particles are in the lowest level, 4 particles are in the first excited state, 2 particles are in the second excited state, and 1 particle is in the third excited state. U = ______ U = ____ Show the system undergoing expansion work by indicating how the energy levels and/or the number of particles in the energy levels might change. Will the temperature of the system stay the same, increase, or decrease? ________ Will the thermodynamic probability stay the same, increase or decrease? _________

## Expert Answer

Answer:

The energy of particle at each level = En = -Rth (1/n2 )

-RH is a constant value of 2.179 x 10-18 Joules

at the ground level 8particle E1 = 8X 2.179X10-18 = -17.432 X 10-18 J

level 2 = 4 particles = E2 = 4X 2.179X10-18 X 4 X (1/4) =-10.87X 10-18J

lvl 3 = 2 particles = E3 = 2 X 2.179X10-18 X 16 X (1/9) = -7.74 X10-18J

lvl 4 = 1 particles = E3 = 1 X 2.179X10-18 X 64 X (1/16) =- 8.716 X 10-18J

DE1-2 = -10.87X 10-18J -( -17.432 X 10-18 J)= 6.56 X 10-18 J

DE1-3 =  -7.74 X10-18J -( -17.432 X 10-18 J)= 9.69 X 10-18 J

DE1-4 =  – 8.716 X 10-18J -( -17.432 X 10-18 J)= 8.716 X 10-18 J

total E change = 24.966X 10-18 J

E is positive, hence the temperature of the system will increase due to expansion work

the thermodynamic probability will increase