A gas in a cylinder expands from a volume of 0.110 m^3 to 0.320 m^3 . Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 * 10^5 Pa during the expansion. The total heat added is 1.15 * 10^5 J. (a) Find the work done by the gas.

Verified step by step guidance

1. Identify the initial and final volumes of the gas. Here, the initial volume $V_i = 0.110 \, \text{m}^3$ and the final volume $V_f = 0.320 \, \text{m}^3$.
2. Recognize that the pressure $P$ remains constant during the expansion, which is given as $P = 1.65 \times 10^5 \, \text{Pa}$.
3. Use the formula for work done by the gas during an isobaric (constant pressure) process, which is $W = P \Delta V$, where $\Delta V = V_f - V_i$ is the change in volume.
4. Substitute the values of $P$, $V_i$, and $V_f$ into the formula to calculate the work done $W$.
5. The work done by the gas can be calculated by finding the product of the constant pressure and the change in volume.

Key Concepts

Work Done by a Gas

In thermodynamics, the work done by a gas during expansion at constant pressure can be calculated using the formula W = PΔV, where W is the work, P is the pressure, and ΔV is the change in volume. This concept is crucial for understanding how gases perform work on their surroundings as they expand.

First Law of Thermodynamics

The First Law of Thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This principle helps in analyzing energy transfers in thermodynamic processes, particularly in understanding how heat and work interact during gas expansion.

Constant Pressure Process

A constant pressure process, also known as isobaric process, occurs when a gas expands or contracts while maintaining the same pressure throughout the process. This condition simplifies calculations of work and heat transfer, as the pressure remains unchanged, allowing for straightforward application of thermodynamic equations.