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Chapter 6: Problem 40

A piston performs work of \(210 . \mathrm{L} \cdot\) atm on the surroundings, while the cylinder in which it is placed expands from \(10 . \mathrm{L}\) to 25 \(\mathrm{L}\) . At the same time, 45 \(\mathrm{J}\) of heat is transferred from the surroundings to the system. Against what pressure was the piston working?

Short Answer

Expert verified
The piston was working against a pressure of approximately 14.00 atm.

Step by step solution

01

Identify the given parameters from the exercise

Work = 210 L·atm Initial volume (V₁) = 10 L Final volume (V₂) = 25 L
02

Find the volume change during the process

We need to find the change in volume during the expansion. ΔV = V₂ - V₁ ΔV = 25 L - 10 L ΔV = 15 L
03

Convert the work from L·atm to J

To find the pressure working against the piston, we need the work to be in Joules. We can use the conversion factor: 1 L·atm = 101.33 J. Work = 210 L·atm × 101.33 J/L·atm Work ≈ 21279.3 J
04

Use the work expression to find the pressure against the piston

Now, we can use the work expression to find the pressure against the piston: Work = Pressure × ΔV Pressure = Work / ΔV Pressure ≈ 21279.3 J / 15 L Pressure ≈ 1418.62 J/L However, the pressure is usually given in atm. We can use the conversion factor: 1 J/L = 0.00986923 atm. Pressure ≈ 1418.62 J/L × 0.00986923 atm/J·L Pressure ≈ 14.00 atm Against what pressure was the piston working? The piston was working against a pressure of approximately 14.00 atm.

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Most popular questions from this chapter

A sample of an ideal gas at 15.0 atm and 10.0 \(\mathrm{L}\) is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature. Calculate the work in units of kJ for the gas expansion. (Hint: Boyle's law applies.)

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