At a constant pressure of 0.905 atm, a chemical reaction...

At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 $\mathrm{cm} .$ During the reaction, the height of the piston drops by 65.0 $\mathrm{cm} .$ (The volume of a cylinder is $V=\pi r^{2} h,$ where $h$ is the height; 1 $\mathrm{L} \cdot$ atm $=$ 101.325 $\mathrm{J.}$ . (a) What is the change in volume in liters during the reaction? (b) What is the value in joules of the work $w$ done during the reaction?

At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 $\mathrm{cm} .$ During the reaction, the height of the piston drops by 65.0 $\mathrm{cm} .$ (The volume of a cylinder is $V=\pi r^{2} h,$ where $h$ is the height; 1 $\mathrm{L} \cdot$ atm $=$ 101.325 $\mathrm{J.}$ .
(a) What is the change in volume in liters during the reaction?
(b) What is the value in joules of the work $w$ done during the reaction?

Key Concepts

Cylindrical Volume Calculation

This concept involves calculating the volume of a cylinder using the formula V = ?r²h. Here, the radius (r) of the cylinder and the height (h) are used to determine how much space is occupied by the substance within the container. Understanding this formula is essential when dealing with volume changes in cylindrical setups such as movable pistons in reaction vessels.

Pressure-Volume Work in Thermodynamics

Pressure-volume work is the work done by or on a system when its volume changes under constant pressure. The work can be calculated using the equation w = -P?V, where P is the pressure and ?V is the change in volume. This concept is key in understanding energy transfer in chemical reactions or physical processes where the volume of the system changes.

Unit Conversion

Proper unit conversion is crucial when calculating and comparing physical quantities. In this context, converting between liter·atm and joules is necessary because while pressure and volume might be given in atmospheres and liters, energy calculations are often required in joules. Understanding the conversion factor (1 L·atm = 101.325 J) helps ensure accurate calculations and meaningful results.

Sign Conventions in Work Calculations

In thermodynamics, the sign of work is important for interpreting the direction of energy transfer. When a system expands, it does work on its surroundings, and the work is often considered positive or negative depending on the convention used. Typically, when the system does work (expansion), the work is defined as negative, and when work is done on the system (compression), it is positive. Recognizing these conventions is essential for correctly applying the work formula in physical and chemical processes.

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