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One mole of an ideal gas at 300 K is reversibly and isothermally compressed from a volume of 20.0 L to a volume of 10.0 L. Because the water bath thermal reservoir in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS system in J/K.

Question

One mole of an ideal gas at 300 K is reversibly and isothermally compressed from a volume of 20.0 L to a volume of 10.0 L. Because the water bath thermal reservoir in the surroundings is very large, T remains essentially constant at 300 K during the process. Calculate ΔS system in J/K.

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Solution

To calculate the change in entropy (ΔS) for an ideal gas during an isothermal process, we can use the formula:

ΔS = nRln(Vf/Vi)

where: n = number of moles R = ideal gas constant Vf = final volume Vi = initial volume

Given in the problem: n = 1 mole R = 8.314 J/(mol·K) (This is the value of R in these units) Vf = 10.0 L Vi = 20.0 L

We can now substitute these values into the formula:

ΔS = 1 mole * 8.314 J/(mol·K) * ln(10.0 L / 20.0 L)

Solving this gives:

ΔS = -1 * 8.314 J/K * ln(0.5)

ΔS = -1 * 8.314 J/K * (-0.6931)

ΔS = 5.76 J/K

So, the change in entropy of the system is 5.76 J/K.

This problem has been solved

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