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One mole of an ideal monoatomic gas expands isothermally against constant external pressure of 1 atm from initial volume of 1L to a state where its final pressure becomes equal to external pressure. If initial temperature of gas is 300 K then total entropy change of system in the above process is : 
[R = 0.082 L atm mol–1 K–1 = 8.3 J mol–1K–1].
a)0
b)R ln (24.6)
c)R ln (2490)
d)
Correct answer is option 'B'. Can you explain this answer?
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Total Entropy Change of the System
To calculate the total entropy change of the system during the isothermal expansion of the ideal monoatomic gas, we can use the following concepts:
Understanding the Process
- The gas expands isothermally at a constant temperature (T = 300 K).
- The initial volume (V1) = 1 L, and it expands against a constant external pressure (P_ext = 1 atm).
- The final pressure of the gas becomes equal to the external pressure.
Final Volume Calculation
- Using the ideal gas law (PV = nRT), we can find the final volume (V2).
- Since P_ext = 1 atm and n = 1 mole, the equation is:
V2 = nRT / P_ext = (1 mol)(0.082 L atm mol–1 K–1)(300 K) / (1 atm) = 24.6 L
Entropy Change Calculation
- The change in entropy (ΔS) for an isothermal process is given by:
ΔS = nR ln(V2/V1)
- Substituting the values:
ΔS = (1 mol)(8.3 J mol–1 K–1) ln(24.6 L / 1 L)
- This simplifies to:
ΔS = 8.3 J mol–1 K–1 * ln(24.6)
Final Result
- Therefore, the total entropy change of the system is:
ΔS = R ln(24.6)
- Thus, the correct answer is option 'B': R ln(24.6).
This indicates that the entropy of the system increases as the gas expands, aligning with the second law of thermodynamics.
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One mole of an ideal monoatomic gas expands isothermally against constant external pressure of 1 atm from initial volume of 1L to a state where its final pressure becomes equal to external pressure. If initial temperature of gas is 300 K then total entropy change of system in the above process is :[R = 0.082 L atm mol–1 K–1 = 8.3 J mol–1K–1].a)0b)R ln (24.6)c)R ln (2490)d)Correct answer is option 'B'. Can you explain this answer?
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