THERM-01 Exam Cheat Sheet

First Law $Q = \Delta U + W \quad \text{Sign: Q>0 absorbed, W>0 expansion, $\Delta U$>0 T rises}$

Four Processes — Zero/Constant Quantity (IAII)

Carnot — KELVIN ONLY $\eta = 1 - \frac{T_2}{T_1} \qquad \text{COP}_{ref} = \frac{T_2}{T_1 - T_2}$

Mayer's Relation $C_p - C_v = R$

Molecular Speeds (ascending) $v_{mp} < v_{avg} < v_{rms} \quad \text{Ratio: } \sqrt{2} : \sqrt{8/\pi} : \sqrt{3} \approx 1 : 1.128 : 1.224$

Degrees of Freedom & γ

Internal Energy $U = \frac{f}{2}nRT \qquad KE_{trans/molecule} = \frac{3}{2}k_BT$

v_rms formula (most-tested) $v_{rms} = \sqrt{\frac{3RT}{M}} \quad [M \text{ in kg/mol}]$

NEET Golden Rules

1. Carnot temperatures MUST be in kelvin (add 273 to °C)
2. Adiabatic ≠ Isothermal: Q = 0 does NOT mean $\Delta T$ = 0
3. Adiabatic curve is always STEEPER than isothermal on PV diagram
4. v_mp < v_avg < v_rms — most probable is SMALLEST
5. COP of refrigerator CAN exceed 1
6. Area under PV curve = Work done by gas