Suppose that you were pumping an automobile tire with a hand...

Suppose that you were pumping an automobile tire with a hand pump that pushed 24.0 in. $^{3}$ of air into the tire on each stroke, and that during one such stroke the opposing pressure in the tire was $30.0 \mathrm{lb} / \mathrm{in} .^{2}$ above the normal atmospheric pressure of $14.7 \mathrm{lb} / \mathrm{in} .^{2} .$ Calculate the number of joules of work accomplished during each stroke. $(1 \mathrm{~L} \mathrm{~atm}=101.325 \mathrm{~J})$

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Key Concepts

Pressure-Volume Work

This concept involves calculating the work done by a system when a volume change occurs under an applied pressure. Mathematically, work (W) is defined as the product of pressure (P) and the change in volume (?V), and ensuring these variables are expressed in consistent units is a key part of solving related problems.

Unit Conversion

Unit conversion is essential when working with measurements that span different systems, such as converting volume from cubic inches to liters or cubic meters, and pressure from lb/in² to atmospheres or pascals. Handling these conversions correctly allows one to use standard conversion factors and obtain accurate results in the desired units.

Energy Conversion

After computing work using pressure-volume work relations, it is often necessary to convert the result into a standard energy unit like the joule. This typically involves applying conversion factors, such as the relationship between liter-atmospheres and joules, to express the work in an internationally accepted unit.

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