A gas expands in volume from 26.7 mL to 89.3 mL at constant temperature. Calculate the work done

step 1 So this question asks us to calculate the work done in joules, given a certain gas expands under

A gas expands in volume from 26.7 mL to 89.3 mL at constant...

A gas expands in volume from $26.7 \mathrm{mL}$ to $89.3 \mathrm{mL}$ at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum, (b) against a constant pressure of $1.5 \mathrm{atm}$, and (c) against a constant pressure of $2.8 \mathrm{atm}$.

A gas expands in volume from $26.7 \mathrm{mL}$ to $89.3 \mathrm{mL}$ at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum,
(b) against a constant pressure of $1.5 \mathrm{atm}$, and
(c) against a constant pressure of $2.8 \mathrm{atm}$.

Key Concepts

Pressure-Volume Work

Pressure-volume work is the energy transferred when a gas expands or compresses. In thermodynamics, work is calculated by integrating the external pressure over the change in volume, which mathematically is represented as w = -? P_ext dV. This concept is essential for understanding the energy changes in processes where gases do work on their surroundings or vice versa.

Work Against a Vacuum

When a gas expands into a vacuum, there is no external pressure opposing its expansion. In such a scenario, the work done by the gas is zero because work is the product of external pressure and the change in volume. This highlights the importance of the environment's resistance in performing work during expansion.

Constant External Pressure Work

For processes occurring at a constant external pressure, the work done by the gas can be calculated directly using the formula w = -P_ext ?V. This simplifies the integration required in variable conditions, making it a straightforward computation of work based on the product of the constant external pressure and the change in volume.

Unit Conversions in Thermodynamics

Accurate calculations in thermodynamics often require converting between different units. For example, converting volume from milliliters to liters and pressure from atmospheres to pascals or joules involves using established conversion factors. Proper unit conversion is crucial to obtaining correct work calculations in consistent energy units, like joules.

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