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Chapter 6: Problem 35

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is \(40 . \mathrm{cm}^{3} .\) If the combustion of this mixture releases 950. J of energy, to what volume will the gases expand against a constant pressure of 650 . torr if all the energy of combustion is converted into work to push back the piston?

Short Answer

Expert verified
The gases will expand to a volume of approximately \(10940 cm^3\) after all the energy from combustion has been converted into work to push back the piston.

Step by step solution

01

Convert energy to work

We are given that the combustion of the mixture releases 950 J of energy, and we will assume that all the energy is converted into work to push back the piston. Work = Energy released by combustion So, Work = 950 J
02

Convert pressure to Pascals

We are given a constant pressure of 650 torr. We need to convert this to Pascals (Pa) to use it further in our calculations. 1 atm = 760 torr 1 atm = 101325 Pa Pressure (Pa) = (Pressure (torr) * 1 atm) / 760 torr * 101325 Pa/atm Pressure (Pa) = (650 * 1 atm) / 760 * 101325 Pa/atm ≈ 87277 Pa
03

Calculate work done against constant pressure

We can calculate the work done against the constant pressure using the following formula: Work = Pressure × Change in Volume We know the Work (950 J) and the Pressure (87277 Pa), so we can calculate the Change in Volume: Change in Volume = Work / Pressure Change in Volume ≈ 950 J / 87277 Pa ≈ 0.0109 m^3
04

Convert original volume to m^3

We are given the original volume in cm^3, and we need to convert it to m^3 to be consistent with the units used above. Original Volume (m^3) = Original Volume (cm^3) * (1 m / 100 cm)^3 Original Volume (m^3) = 40 cm^3 * (1 m / 100 cm)^3 ≈ 4.0 × 10^-5 m^3
05

Calculate the final volume

Now we can add the Change in Volume to the Original Volume to find the Final Volume: Final Volume (m^3) = Original Volume (m^3) + Change in Volume (m^3) Final Volume (m^3) ≈ 4.0 × 10^-5 m^3 + 0.0109 m^3 ≈ 0.01094 m^3
06

Convert final volume back to cm^3

Finally, we will convert the Final Volume back to cm^3 to match the given units: Final Volume (cm^3) = Final Volume (m^3) * (100 cm / 1 m)^3 Final Volume (cm^3) ≈ 0.01094 m^3 * (100 cm / 1 m)^3 ≈ 10940 cm^3 The gases will expand to a volume of approximately 10940 cm^3 after all the energy from combustion has been converted into work to push back the piston.

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