A sample gas undergoes adiabatic process which is compressed from 900 cm to 450 cm. How much work is done by the gas if initial pressure is 150 122 Take Y as 1.3.

To determine the work done by a gas during an adiabatic compression, we can use the principles of thermodynamics. In an adiabatic process, there is no heat exchange with the surroundings, and the work done on the gas results in a change in its internal energy. The formula for work done during an adiabatic process can be derived from the first law of thermodynamics and the ideal gas law.

Understanding the Variables

In this scenario, we have the following parameters:

• Initial volume (V1): 900 cm³
• Final volume (V2): 450 cm³
• Initial pressure (P1): 150 kPa
• Adiabatic index (Y): 1.3

Work Done in an Adiabatic Process

The work done (W) on the gas during an adiabatic process can be calculated using the formula:

W = (P1 * V1 - P2 * V2) / (Y - 1)

To use this formula, we first need to find the final pressure (P2) after the compression. We can use the adiabatic condition:

P1 * V1^Y = P2 * V2^Y

Calculating Final Pressure (P2)

Substituting the known values into the equation:

150 kPa * (900 cm³)^1.3 = P2 * (450 cm³)^1.3

Calculating the left side:

150 * 900^1.3 ≈ 150 * 1897.1 ≈ 284565 kPa

Now, we can solve for P2:

P2 = 284565 kPa / (450 cm³)^1.3

Calculating the denominator:

(450 cm³)^1.3 ≈ 450 * 117.5 ≈ 52875 kPa

Now substituting back:

P2 ≈ 284565 kPa / 52875 ≈ 53.8 kPa

Calculating Work Done (W)

Now that we have P2, we can substitute P1, P2, V1, and V2 into the work formula:

W = (150 kPa * 900 cm³ - 53.8 kPa * 450 cm³) / (1.3 - 1)

Calculating the terms:

• 150 kPa * 900 cm³ = 135000 kPa·cm³
• 53.8 kPa * 450 cm³ = 24110 kPa·cm³

Now substituting these values:

W = (135000 - 24110) / 0.3

W = 110890 / 0.3 ≈ 369630 kPa·cm³

Final Result

The work done by the gas during this adiabatic compression is approximately 369630 kPa·cm³. This value indicates the energy transferred to the gas as it is compressed, reflecting the relationship between pressure, volume, and the adiabatic nature of the process.