If there are 2 mole of gas kept at a constant temperature of 20⁰C and if this gas is compressed from a volume of 4m³ to 2m³, calculate the work done on the gas.

To calculate the work done on a gas during compression, we can use the formula derived from the ideal gas law and the principles of thermodynamics. In this case, since the temperature is constant, we are dealing with an isothermal process. The work done on the gas can be calculated using the equation:

Work Done on the Gas

The formula for work done (W) during an isothermal process is given by:

W = -PΔV

Where:

• P is the pressure of the gas.
• ΔV is the change in volume (final volume - initial volume).

Step 1: Calculate the Change in Volume

First, we need to determine the change in volume (ΔV). Given that the initial volume (V1) is 4 m³ and the final volume (V2) is 2 m³, we can calculate:

ΔV = V2 - V1 = 2 m³ - 4 m³ = -2 m³

Step 2: Determine the Pressure of the Gas

Next, we need to find the pressure (P) of the gas. We can use the ideal gas law, which states:

PV = nRT

Where:

• P is the pressure.
• V is the volume.
• n is the number of moles (2 moles in this case).
• R is the ideal gas constant (approximately 8.314 J/(mol·K)).
• T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin:

T = 20°C + 273.15 = 293.15 K

Now, we can rearrange the ideal gas law to solve for pressure:

P = nRT / V

Substituting the known values:

P = (2 moles) × (8.314 J/(mol·K)) × (293.15 K) / (4 m³)

Calculating this gives:

P ≈ 1.25 × 10^3 Pa (Pascals)

Step 3: Calculate the Work Done

Now that we have both the pressure and the change in volume, we can substitute these values back into the work formula:

W = -PΔV

Substituting the values:

W = - (1.25 × 10^3 Pa) × (-2 m³)

Calculating this gives:

W = 2.5 × 10^3 J

Final Result

The work done on the gas during the compression from 4 m³ to 2 m³ at a constant temperature of 20°C is approximately 2500 Joules. This positive value indicates that work is done on the gas, which is consistent with the process of compression.