A 2.10-mole sample of an ideal gas is allowed to expand at a constant temperatur

Question

A 2.10-mole sample of an ideal gas is allowed to expand at a constant temperature of 278 K. The initial volume is 14.5 L and the gas performs 945 J of work. What is the final volume of the container? Let the ideal-gas constant R = 8.314 J/(mol • K).

19.5 L

17.6 L

22.3 L

28.4 L

A 2.10-mole sample of an ideal gas is allowed to expand at a constant temperature of 278 K. The initial volume is 14.5 L and the gas performs 945 J of work. What is the final volume of the container? Let the ideal-gas constant R = 8.314 J/(mol • K).

19.5 L

17.6 L

22.3 L

28.4 L

Explanation / Answer

let the final voluem is Vf

initial volume , Vi = 14.5 L

temperature , T = 278 K

at constant temperatre ,

work done = n * R * T * ln(Vf/Vi)

work done = 2.1 * 8.314 * 278 * ln(Vf/14.5)

945 = 2.1 * 8.314 * 278 * ln(Vf/14.5)

solving for Vf

Vf = 17.6 Litre

the final volume of gas is 17.6 L

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