Consider equal amount of two identical ideal gases at the same temperature T but at different pressure P1andP2, two different containers of volume V1andV2 respectively, which are joined by the partition. Starting with sackur-tetrode relation prove that if gases are allowed to mix each other by removing the partition between them to change in the entropy is given by S=N*K ln[(P1+P2)^2/(4*P1*P2)] assume that the temperature remain the same after mixing of the ideal?

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Consider equal amount of two identical ideal gases at the same temperature T but at different pressure P1&P2, two different containers of volume V1&V2 respectively, which are joined by the partition. Starting with sackur-tetrode relation prove that if gases are allowed to mix each other by removing the partition between them to change in the entropy is given by S=N*K ln[(P1+P2)^2/(4*P1*P2)] assume that the temperature remain the same after mixing of the ideal?

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Consider equal amount of two identical ideal gases at the same tempera...

Sackur-Tetrode Relation:

The Sackur-Tetrode equation gives the entropy of an ideal gas in terms of its thermodynamic properties. It is given by:

S = Nk [ln(V/N) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

where S is the entropy, N is the number of particles, k is the Boltzmann constant, V is the volume, T is the temperature, m is the mass of a single particle, and h is the Planck constant.

Entropy Change when Mixing Gases:

When two ideal gases are allowed to mix, the total entropy change can be calculated by considering the change in volume and pressure. Let's assume that the initial pressure and volume of the gases are P1, V1, and P2, V2 respectively.

The total entropy change can be calculated by summing the entropy changes of the individual gases before and after mixing. The entropy change for each gas can be calculated using the Sackur-Tetrode equation.

Entropy Change of Gas 1:

The initial entropy of Gas 1 is given by:

S1_initial = N1k [ln(V1/N1) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

After mixing, the volume becomes V1 + V2 and the pressure becomes the average of the initial pressures, (P1 + P2)/2.

The final entropy of Gas 1 is given by:

S1_final = N1k [ln((V1 + V2)/N1) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

Entropy Change of Gas 2:

Similarly, the initial and final entropies for Gas 2 can be calculated as:

S2_initial = N2k [ln(V2/N2) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

S2_final = N2k [ln((V1 + V2)/N2) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

Total Entropy Change:

The total entropy change is the sum of the entropy changes of Gas 1 and Gas 2:

ΔS_total = S1_final - S1_initial + S2_final - S2_initial

Simplifying the above equation and substituting the values, we get:

ΔS_total = Nk [ln((V1 + V2)/(N1 + N2)) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

Since we have equal amounts of the two gases, N1 = N2 = N, and the equation further simplifies to:

ΔS_total = Nk [ln((V1 + V2)/N) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

Simplifying the natural logarithm terms, we get:

ΔS_total = Nk [ln(V1 + V2) - ln(N) + 5/2 ln(T) + ln(4πm/3h^2)^3/2]

Using the properties of logarith

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Consider equal amount of two identical ideal gases at the same temperature T but at different pressure P1&P2, two different containers of volume V1&V2 respectively, which are joined by the partition. Starting with sackur-tetrode relation prove that if gases are allowed to mix each other by removing the partition between them to change in the entropy is given by S=N*K ln[(P1+P2)^2/(4*P1*P2)] assume that the temperature remain the same after mixing of the ideal? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Consider equal amount of two identical ideal gases at the same temperature T but at different pressure P1&P2, two different containers of volume V1&V2 respectively, which are joined by the partition. Starting with sackur-tetrode relation prove that if gases are allowed to mix each other by removing the partition between them to change in the entropy is given by S=N*K ln[(P1+P2)^2/(4*P1*P2)] assume that the temperature remain the same after mixing of the ideal? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider equal amount of two identical ideal gases at the same temperature T but at different pressure P1&P2, two different containers of volume V1&V2 respectively, which are joined by the partition. Starting with sackur-tetrode relation prove that if gases are allowed to mix each other by removing the partition between them to change in the entropy is given by S=N*K ln[(P1+P2)^2/(4*P1*P2)] assume that the temperature remain the same after mixing of the ideal?.

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