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Suppose that 2 kg of \(O_2\) gas are allowed to expand isothermally at \(T = 127^\circ C\) from an initial volume of 10 liters to a final volume of 60 liters. How much work does the gas do on the piston?

Select one:
A. 372 kJ
B. 272 kJ
C. 172 kJ
D. 472 kJ

Answer :

The answer is option A, 372 kJ. In an isothermal process, the temperature remains constant throughout the process.

The work done by the gas on the piston can be calculated by using the formula of work for a gas: W = nRT ln(V2/V1).

Here, n is the number of moles of gas, R is the universal gas constant, T is the temperature in Kelvin, and V2 and V1 are the final and initial volumes of the gas, respectively.

Using the given values: n = m/M = 2000/32 = 62.5 moles (where m is the mass of O2 gas, and M is the molar mass of O2), R = 8.31 J/mol K, T = 127 + 273 = 400 K, V2 = 60 L, V1 = 10 L

The work done by the gas on the piston is: W = nRT ln(V2/V1)W = 62.5 x 8.31 x 400 ln(60/10)W = 372,097.5 J = 372 kJ

Therefore, the answer is option A, 372 kJ.

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