Isothermal Expansion of an Ideal Gas
This article will explore the isothermal expansion of an ideal gas from an initial volume of 10⁻³ m³ to a final volume of 10⁻² m³ at a constant temperature of 300 K.
Understanding Isothermal Processes
An isothermal process is a thermodynamic process that occurs at a constant temperature. In this scenario, the gas expands while maintaining a constant temperature. This implies that any heat absorbed by the gas during the expansion is immediately transferred to the surroundings, preventing a temperature change.
Applying the Ideal Gas Law
The ideal gas law, given by PV = nRT, helps us analyze the behavior of the gas during this process. Where:
- P is the pressure of the gas.
- V is the volume of the gas.
- n is the number of moles of the gas.
- R is the ideal gas constant (8.314 J/mol·K).
- T is the temperature of the gas.
Since the temperature remains constant, we can simplify the ideal gas law for our scenario:
P₁V₁ = P₂V₂
Where:
- P₁ is the initial pressure.
- V₁ is the initial volume (10⁻³ m³).
- P₂ is the final pressure.
- V₂ is the final volume (10⁻² m³).
Calculating the Final Pressure
Using the simplified ideal gas law, we can calculate the final pressure of the gas:
P₂ = (P₁V₁)/V₂
Substituting the given values:
P₂ = (P₁ * 10⁻³ m³)/10⁻² m³ = P₁/10
This implies that the final pressure is one-tenth of the initial pressure.
Work Done During Expansion
During isothermal expansion, the gas does work on the surroundings. The work done is given by:
**W = nRT ln(V₂/V₁) = P₁V₁ ln(V₂/V₁) **
Where:
- W is the work done.
- ln is the natural logarithm.
Substituting the given values:
W = P₁ * 10⁻³ m³ * ln(10⁻² m³/10⁻³ m³) = P₁ * 10⁻³ m³ * ln(10)
Therefore, the work done by the gas during this isothermal expansion is equal to P₁ * 10⁻³ m³ * ln(10).
Conclusion
The isothermal expansion of an ideal gas from 10⁻³ to 10⁻² m³ at 300 K results in a decrease in pressure to one-tenth of the initial pressure. The gas performs work on the surroundings during the expansion, the amount of which is dependent on the initial pressure. Understanding these concepts allows us to predict and analyze the behavior of gases undergoing isothermal processes.
