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A sample of an ideal gas with initial pressure p and volume V is taken through an isothermal expansion proceed during which the change in entropy is found to be ΔS. The universal gas constant is R. Then, the work done by the gas is given by
Select one:
  • a)
    nRΔS
  • b)
    pΔS\nRV
  • c)
    pV
  • d)
    pVΔS\nR
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A sample of an ideal gas with initial pressure p and volume V is taken...
By ideal gas equal,
pV = nRT

Multiplying both the equations,
pVΔS = nRΔQ

∴ For isothermal expansion, ΔT = 0

The correct answer is: pVΔS\nR
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Most Upvoted Answer
A sample of an ideal gas with initial pressure p and volume V is taken...
To find the change in entropy during an isothermal expansion, we can use the equation:

ΔS = nR ln(Vf/Vi)

Where:
ΔS is the change in entropy
n is the number of moles of gas
R is the gas constant
Vf is the final volume
Vi is the initial volume

Given that the initial pressure is p and the initial volume is V, we need to assume the number of moles of gas in order to find the change in entropy.

Let's assume that the number of moles of gas is represented by 'n'. Therefore, the change in entropy can be written as:

ΔS = nR ln(Vf/Vi)

We can rearrange this equation to solve for the final volume:

Vf = Vi * e^(ΔS/(nR))

Therefore, the final volume of the gas can be calculated using this equation.
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A sample of an ideal gas with initial pressure p and volume V is taken through an isothermal expansion proceed during which the change in entropy is found to be ΔS. The universal gas constant is R. Then, the work done by the gas is given bySelect one:a)nRΔSb)pΔS\nRVc)pVd)pVΔS\nRCorrect answer is option 'D'. Can you explain this answer?
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