Gas Thermodynamics Lab: Verification of Boyle's Law
Investigate **Boyle's Law**, which states that for a fixed mass of gas at constant temperature, the pressure ($P$) is inversely proportional to the volume ($V$), or **$PV = \text{constant}$**.
Key Equations & Concepts
▼$$ P_1 V_1 = P_2 V_2 $$ (At constant Temperature and mass)
A process occurring at **constant temperature ($T$)**. The work done ($W$) during a reversible isothermal expansion is: $$ W = nRT \ln\left(\frac{V_2}{V_1}\right) $$
$$ PV = nRT $$ (This foundational equation is derived from the Gas Laws).
Experiment 1: Pressure-Volume Relation Simulator
Adjust the pressure applied to the piston and observe the resulting volume and $PV$ constant.
Volume is inversely proportional to Pressure.
Experiment 2: Isothermal Work & Final State Challenge
Calculate the final volume ($V_2$) and the Work Done ($W$) during an isothermal 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
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.
- **Charles's Law:** $V \propto T$ (at constant $P$).
- **Gay-Lussac's Law:** $P \propto T$ (at constant $V$).
In the isothermal process, since $\Delta T = 0$, the change in internal energy ($\Delta U$) is zero ($\Delta U \propto \Delta T$). Therefore, by the First Law of Thermodynamics ($\Delta Q = \Delta U + \Delta W$), all heat supplied ($\Delta Q$) is converted into work done ($\Delta W$).
