Calculate the stress for 1L of a perfect gas at a pressure of 72 mm Hg, when it is compressed isothermally to a volume of 900 cc

1. 9.88×10³ N/m²
2. 10.88×10³ N/m²
3. 1.088×10^{3 N/m2}
4. N.O.T.

To calculate the stress of a perfect gas when it is compressed isothermally, we can use the ideal gas law and the relationship between pressure, volume, and stress. Stress in this context can be understood as the pressure exerted by the gas on the walls of its container. Let's break this down step by step.

Understanding the Ideal Gas Law

The ideal gas law is expressed as:

PV = nRT

Where:

• P = pressure (in pascals)
• V = volume (in cubic meters)
• n = number of moles of gas
• R = ideal gas constant (8.314 J/(mol·K))
• T = temperature (in kelvins)

Given Values

In this scenario, we have:

• Initial pressure, P1 = 72 mm Hg
• Initial volume, V1 = 1 L = 0.001 m³
• Final volume, V2 = 900 cc = 0.0009 m³

Converting Pressure Units

First, we need to convert the pressure from mm Hg to pascals. The conversion factor is:

1 mm Hg = 133.322 Pa

Thus, the initial pressure in pascals is:

P1 = 72 mm Hg × 133.322 Pa/mm Hg = 9605.184 Pa

Applying the Ideal Gas Law

Since the process is isothermal, we can use the relationship between the initial and final states of the gas:

P1 × V1 = P2 × V2

We can rearrange this to find the final pressure (P2):

P2 = (P1 × V1) / V2

Substituting the known values:

P2 = (9605.184 Pa × 0.001 m³) / 0.0009 m³

P2 = 10673.538 Pa

Calculating Stress

Stress in this context is equivalent to the pressure exerted by the gas, which we have calculated as P2. Therefore, the stress is:

Stress = P2 = 10673.538 Pa

Final Result

To express this in a more manageable form, we can convert it to kilopascals:

Stress = 10.67 kPa

So, the stress for 1L of a perfect gas at a pressure of 72 mm Hg, when compressed isothermally to a volume of 900 cc, is approximately 10.67 kPa.