Error Analysis: Common Mistakes

Error Analysis Table (8 Major Errors)

#	Common Error	What Students Do	Why It's Wrong	Correct Approach
1	Celsius in Carnot	η = 1 − 27/127 = 78.7%	Carnot formula requires absolute temperature (kelvin)	Always convert: T(K) = T(°C) + 273. η = 1 − 300/400 = 25%
2	Adiabatic = isothermal	Conclude T is constant in adiabatic because Q = 0	Q = 0 means no heat exchange, not no temperature change	In adiabatic: $\Delta U$ = −W. Expansion → W > 0 → $\Delta U$ < 0 → T decreases
3	Wrong sign for W	W = nRT ln( $V_{1}$ / $V_{2}$ ) instead of ln( $V_{2}$ / $V_{1}$ )	Inverted logarithm ratio	W = nRT ln( $V_{2}$ / $V_{1}$ ). Expansion ( $V_{2}$ > $V_{1}$ ): W > 0. Compression: W < 0.
4	$\Delta U$ ≠ 0 for isothermal	Write $\Delta U$ = nCᵥ $\Delta T$ even for isothermal	For ideal gas, U depends only on T. If T constant, $\Delta U$ = 0	$\Delta U$ = 0 for isothermal process of ideal gas regardless of formula used
5	Forgetting γ in adiabatic	Use PV = const instead of PV^γ = const	Adiabatic ≠ isothermal. Extra γ from the coupled $\Delta U$ term	Adiabatic: PV^γ = const. Isothermal: PV = const. γ > 1 always.
6	v_mp > v_rms	Reverse the speed order	Confusion about "most probable" vs "maximum"	Always: v_mp < v_avg < v_rms. RMS is largest because $v^{2}$ weighting elevates it.
7	C_p = C_v for any gas	Assume C_p = C_v	Extra work done at constant pressure requires extra heat	C_p − C_v = R (Mayer's relation). C_p > C_v always for any ideal gas.
8	Wrong γ for gas type	Use γ = 5/3 for diatomic gas	Monoatomic: f = 3, γ = 5/3. Diatomic: f = 5, γ = 7/5 = 1.4	Identify gas type first. Monoatomic: He, Ar. Diatomic: $O_{2}$ , $N_{2}$ , $H_{2}$ .
9	Treating polyatomic as diatomic	Use f = 5 for C $O_{2}$	C $O_{2}$ is polyatomic (nonlinear): f = 6, γ = 4/3	Check molecular type. C $O_{2}$ , $H_{2}$ O, $NH_{3}$ : f = 6 (3 trans + 3 rot).