How much work is done by a gas whose inital volume is 3 litre , and whose temp. increases 27(dgre) C to 227(dgre) c, pressure remaining constant at 2.0 *10000 P.a ?

To determine the work done by a gas during an expansion at constant pressure, we can use the formula for work done in a thermodynamic process. The work done (W) by a gas when it expands or contracts at constant pressure is given by:

Work Done by the Gas

The formula for work done is:

W = P × ΔV

Where:

• W = work done (in joules)
• P = pressure (in pascals)
• ΔV = change in volume (in cubic meters)

Step-by-Step Calculation

1. **Convert the initial volume from liters to cubic meters**: Since 1 liter is equal to 0.001 cubic meters, we can convert the initial volume:

Initial Volume (V1) = 3 liters = 3 × 0.001 = 0.003 m³

2. **Determine the final volume using the ideal gas law**: Since the pressure remains constant, we can use the relationship between temperature and volume. According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin.

First, convert the temperatures from Celsius to Kelvin:

• T1 = 27°C = 27 + 273.15 = 300.15 K
• T2 = 227°C = 227 + 273.15 = 500.15 K

3. **Calculate the final volume (V2)**: Using the formula:

V2 = V1 × (T2 / T1)

Substituting the values:

V2 = 0.003 m³ × (500.15 K / 300.15 K) ≈ 0.005 m³

4. **Calculate the change in volume (ΔV)**:

ΔV = V2 - V1 = 0.005 m³ - 0.003 m³ = 0.002 m³

5. **Calculate the work done (W)**: Now, we can substitute the values into the work formula. The pressure given is 2.0 × 10,000 Pa = 20,000 Pa.

W = P × ΔV = 20,000 Pa × 0.002 m³ = 40 J

Final Result

The work done by the gas during this process is 40 joules.

This calculation illustrates how changes in temperature and volume at constant pressure can lead to work being done by the gas. It's a fundamental concept in thermodynamics that helps us understand energy transfer in gases.