How much work (in J) is required to expand the volume of a pump from 0.0 L to 2.5 L against an external pressure of 1.1 atm?

검증된 단계별 안내

Identify the formula for work done during expansion: \( W = -P_{\text{ext}} \Delta V \), where \( W \) is work, \( P_{\text{ext}} \) is the external pressure, and \( \Delta V \) is the change in volume.

Calculate the change in volume \( \Delta V \) by subtracting the initial volume from the final volume: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 2.5 \text{ L} - 0.0 \text{ L} \).

Convert the external pressure from atm to the SI unit of pressure, pascals (Pa), using the conversion factor: \( 1 \text{ atm} = 101325 \text{ Pa} \).

Convert the volume change from liters to cubic meters (m³) since 1 L = 0.001 m³.

Substitute the values into the work formula and solve for \( W \), ensuring all units are consistent (pressure in Pa and volume in m³).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gas expansion, the work done on or by the system can be calculated using the formula W = -P_extΔV, where P_ext is the external pressure and ΔV is the change in volume. The negative sign indicates that work is done by the system when it expands.

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts against an external pressure. It is a common type of work in chemical processes, particularly in engines and pumps. The work done can be expressed in units of energy, such as joules, and is directly related to the pressure exerted and the change in volume of the gas.

Unit Conversion

In this problem, it is essential to convert pressure from atmospheres to joules. The conversion factor is 1 atm = 101.325 J/L. This conversion allows for consistent units when calculating work, ensuring that the pressure and volume are compatible in the formula used to determine the work done during the expansion.