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A gas expands from 30L to 50L against a constant pressure of 1atm. What is the calculated value for work? Report your answer in kJ to the nearest whole number.

a) 20kJ

b) −20kJ

c) 50kJ

d) −50kJ

1 Answer

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Final answer:

The work done by the gas during expansion is -2 kJ to the nearest whole number, after converting the pressure and volume to SI units and using the formula for work at constant pressure.

Step-by-step explanation:

The work done by a gas during expansion or compression can be calculated using the formula work = -P∆V, where P is the constant external pressure and ∆V is the change in volume. In this case, a gas expands from 30L to 50L against a constant pressure of 1 atm. So, ∆V is 50L - 30L = 20L. We will convert the volumes to the proper units of cubic meters using the conversion factor 1L = 0.001 m³, and the pressure to pascals using 1 atm = 101,325 Pa. The work done by the gas can be calculated in joules (J) and then converted to kilojoules (kJ) using 1 kJ = 1000 J.

The calculated value for work is:

work = -P∆V

work = -(1 atm)(20L)

work = -(101,325 Pa)(0.020 m³)

work = -2026.5 J

work = -2.0265 kJ

Rounding this to the nearest whole number, the work done by the gas is -2 kJ. Since work is done by the system (the gas), it is considered negative, which means option b) -20kJ is almost correct, but because we are asked to round to the nearest whole number the correct answer is a) -2kJ (not listed among the options provided). The magnitude is correct but the unit's order of magnitude is off by a factor of ten in the options provided.

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