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Multiple Choice
3 moles of an ideal gas are compressed isothermally at 20°C. During this compression, 1850 J of work is done on the gas. What is the change of entropy of the gas?
A
–24.9 J/K
B
6.31 J/K
C
–6.31 J/K
D
–9158 J/K
Verified step by step guidance
1
Identify the process: The gas is compressed isothermally, meaning the temperature remains constant throughout the process.
Recall the formula for the change in entropy (ΔS) for an isothermal process: ΔS = \( \frac{Q}{T} \), where Q is the heat exchanged and T is the absolute temperature in Kelvin.
Since the process is isothermal, use the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done on the system. For an ideal gas in an isothermal process, ΔU = 0, so Q = W.
Convert the given temperature from Celsius to Kelvin: T(K) = 20°C + 273.15 = 293.15 K.
Substitute the known values into the entropy change formula: ΔS = \( \frac{1850 \text{ J}}{293.15 \text{ K}} \). Calculate this expression to find the change in entropy.