Investigating Microstates And Macrostates Using Random Number Generator

The histograms can be drawn as

The values of each microstate and the standard deviation are calculated and it seems like the same values will be obtained from wiggley-eyes. 

1. The micro states for each state are calculated in the excel and the same is attached as-

2. The spreadsheet with data is attached below-

The entropy curves can be generated as-

The second curve for the multiplicity can be drawn as-

1. The limitations of the spreadsheet program are as follows-
2. Calculated values may differ by standard deviation.
3. Curve start and end point cannot be adjusted to make it more presentable.

Answer 3

Quasistatic process-

1. The given equation is as follows-And  Also, 

1. For the adiabatic process- 

Answer 4

The given Carnot cycle is as follows-

1. The heats associated for the process AB and CD- 

1. The relation between P and V for processes AB, BC, CD and DA-

For process AB- 

For process BC- 

For process CD- 

For process DA- 

1. The efficiency of the cycle can be calculated as-

Answer 5

1. The energy gained from ice melting- 

1. Energy gained by melted ice-

1. The energy lost by lemonade- 

1. Specific heat of lemonade c = 4.2 kJ/kgK 

Gibbs free energy

The given data are as follows-

The Gibbs free energy of mixing-

Now considering the pseudobinary alloy- 

Part a

The probability of each Tetrahydron can be calculated as- 

Part b

1. The number of microstates can be calculated as- 

1. The entropy of mixing- 

Yes, the entropy of the mixing will be depending on the fraction and thus the expression expresses the mixing entropy in correct way. 

Part c

1. The enthalpy of mixing in random approximation can be calculated as- 

Where w is the energy required and can be calculated as- 

The expression is the sum of 5 states of the random number approximation. 

1. The given data are as follows-

T = 200 K and T = 300 K

n = 1 mole

 alloy at x = 0.25 

Now the Gibbs free energy can be calculated as- …………….i 

 Now substituting all values in equation i-

For T = 200 K:  

For T = 300 K: 

At 300 K the Gibbs free energy is less as compared to the Gibbs free energy at 200K and thus it will be less stable at 200 K.

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