1 mole of an ideal gas at 25°C is subjected to expands reversibly 10 times of its initial volume. What is the change in entropy _________ JK-1
Question
1 mole of an ideal gas at 25°C is subjected to expands reversibly 10 times of its initial volume. What is the change in entropy _________ JK-1
Solution
To calculate the change in entropy, we can use the formula:
ΔS = nR ln(Vf/Vi)
Where: ΔS is the change in entropy n is the number of moles of the gas R is the ideal gas constant (8.314 J/(mol·K)) Vf is the final volume Vi is the initial volume
Given that we have 1 mole of gas and it expands 10 times its initial volume, we can say that Vf = 10Vi.
Substituting these values into the formula, we have:
ΔS = (1 mol)(8.314 J/(mol·K)) ln(10Vi/Vi)
Simplifying the expression, we get:
ΔS = 8.314 J/K ln(10)
Using the natural logarithm of 10, we find:
ΔS ≈ 8.314 J/K (2.3026)
Calculating this, we find:
ΔS ≈ 19.14 J/K
Therefore, the change in entropy is approximately 19.14 J/K.
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