= Isothermal gas syringe experiment
A <gas syringe> makes the distinction between a constant-<temperature> path and equal-<temperature> endpoints observable. The <Ideal Gas Law Apparatus (TD-8596A), Instruction Manual 012-08420B by PASCO scientific> specifies a TD-8596A <gas syringe> with a mechanical stop, an internal thermistor, an attached <pressure> sensor and data acquisition. Record the stop <volume (thermodynamics)> with the coupling disconnected, then set $40\,\mathrm{mL}$ and seal the coupling. Record <pressure> and <temperature>, compress quickly to the stop near $20\,\mathrm{mL}$, and hold until both readouts settle. The manual gives roughly $30\,\mathrm s$ for settling and about $0.5\,\mathrm s$ for the thermistor response. Releasing the plunger gives a second transient and a final <volume (thermodynamics)> to record.<Ideal Gas Law Apparatus (TD-8596A), Instruction Manual 012-08420B by PASCO scientific>[pp. 2–4: Introduction, Equipment Setup and Experiment 1 procedure]{ref}
The manual describes a <pressure> overshoot and <temperature> rise during rapid compression, followed by cooling at the held <volume (thermodynamics)>; the settled <pressure> remains higher than initially. This illustrates approximately <adiabatic compression> followed by <heat> rejection, rather than an <isothermal compression> throughout. Use the settled initial and compressed readings to test <Boyle's law>, correcting both syringe readings by the unmarked tubing <volume (thermodynamics)> $V_d$:
$$
p_i(V_{\rm read,i}+V_d)=p_f(V_{\rm read,f}+V_d).
$$
Use <absolute pressure>, not <gauge pressure>. A transient comparison of $pV/T$ must pair simultaneous <pressure> and <temperature> readings: the sensor lag can separate their peaks.<Ideal Gas Law Apparatus (TD-8596A), Instruction Manual 012-08420B by PASCO scientific>[pp. 4–5: Constant Temperature and Varying Temperature analyses; p. 8: answers 1–3]{ref}
For an additional test of the path, repeat with small compression steps, wait for stable <temperature> and <pressure> at every step, and repeat in reverse. Keep the sealed <amount of substance>, connecting tubing and ambient <temperature> fixed; prevent hand warming of the barrel and check for leaks by watching for continued <pressure> drift at held <volume (thermodynamics)> after <thermal equilibrium>. These are proposed controls, rather than reported measurements. Agreement of equilibrated points with <Boyle's law> supports the fixed-<temperature> <ideal gas law> approximation, but does not prove that the rapid segments between them were <isothermal processes>. A single local <temperature> sensor can miss <temperature gradients>; plunger <friction> can produce direction-dependent readings. The <pressure> and <volume (thermodynamics)> data estimate reversible <work> only insofar as the path approaches a <reversible thermodynamic process>; they do not directly measure <heat>. After motion stops, cooling at fixed <volume (thermodynamics)> has zero boundary <work> and $Q=\Delta U<0$, even though the complete equal-endpoint-<temperature> <ideal gas> run has $\Delta U=0$.
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