Gas Thermodynamics Lab: Verification of Boyle's Law and Isothermal Work
Investigate **Boyle's Law** ($PV = \text{constant}$) and calculate the **Work Done ($W$)** during a reversible **isothermal expansion or compression** process.
Key Equations & Concepts
▼$$ P_1 V_1 = P_2 V_2 $$ (At constant Temperature and mass)
$$ W = - nRT \ln\left(\frac{V_2}{V_1}\right) $$ (Challenge uses the magnitude: $|W| = nRT \ln(V_{final}/V_{initial})$)
- $R = 8.314 \text{ J/mol}\cdot\text{K}$
- Challenge uses $n=1 \text{ mole}$ and $T=300 \text{ K}$
Experiment 1: Boyle's Law Verification (Isothermal Process)
Adjust the pressure applied to the piston and verify the constancy of the $PV$ product.
Volume is inversely proportional to Pressure (at $T=300 \text{ K}$).
Experiment 2: Isothermal Work & Final State Challenge
Calculate the final volume ($V_2$) and the **Work Done ($W$)** magnitude during the process.
Boyle's Law only holds true if the temperature is strictly constant. When pressure is rapidly increased (volume decreased), the gas temperature tends to rise. Therefore, the experiment must be done slowly (quasi-statically) or the system must be allowed to exchange heat with the surroundings.
Kinetic Theory and Microscopic View
$$ |W| = |nRT \ln\left(\frac{V_2}{V_1}\right)| $$ The magnitude of work measures the energy transferred, regardless of whether it's compression (positive W) or expansion (negative W).
When the volume ($V$) of a container decreases, gas molecules collide with the walls **more frequently**. Since pressure is directly proportional to the collision frequency, pressure ($P$) increases, confirming the inverse relationship.
Because the temperature is constant in an isothermal process, the change in internal energy ($\Delta U$) is **zero** ($\Delta U=0$).
