Thermodynamics

Thermodynamics relates heat, work, internal energy, and temperature. For the MCAT Chemical and Physical Foundations section, know the temperature scales, the zeroth/first/second laws, calorimetry (q = mcΔT), latent heat of phase changes, work by a gas on PV diagrams, entropy, and the three modes of heat transfer. Numerical items are high-yield and strictly algebra-based (no calculus).

MCAT content mapping. Thermodynamics spans temperature & the zeroth law, heat transfer (conduction, convection, radiation), specific & latent heat, the first law (ΔU = Q − W), PV work and processes, the second law & entropy, and heat engines/efficiency.

Temperature & Its Scales

Temperature measures the average translational kinetic energy of the particles of a substance. Three scales appear on the MCAT:

Celsius (°C): water freezes at 0°C, boils at 100°C.
Kelvin (K): the absolute scale; 0 K = absolute zero = −273.15°C. Same size degree as Celsius: T(K) = T(°C) + 273.15. Always use kelvin in gas-law and efficiency formulas.
Fahrenheit (°F): T(°F) = (9/5)T(°C) + 32.

A change of 1°C equals a change of 1 K (but a change of 1.8°F).

Thermal Equilibrium and Heat

Two bodies are in thermal equilibrium when there is no net flow of heat between them — equivalently, they have the same temperature. The Zeroth Law of Thermodynamics: if A is in thermal equilibrium with C and B is in thermal equilibrium with C, then A is in thermal equilibrium with B. This justifies the very concept of temperature.

Heat (Q) is energy in transit between systems due to a temperature difference. SI unit: joule (J). 1 calorie = 4.18 J. Heat is a process quantity (path-dependent), not a state function.

Internal energy

Internal energy U is the total kinetic + potential energy of all the molecules in a system. It is a state function — depends only on the present state, not the history. For an ideal gas U depends only on temperature.

Specific Heat, Calorimetry & Latent Heat

To raise the temperature of a substance (no phase change), the heat required is:

q = mcΔT

where m is mass, c is the specific heat (J/(kg·K) or J/(g·°C)), and ΔT is the temperature change. Water has an unusually large specific heat, c ≈ 4.18 J/(g·°C) — important for biological temperature buffering. Calorimetry uses conservation of energy: heat lost by the hot object = heat gained by the cold object (q_lost + q_gained = 0).

During a phase change temperature stays constant while heat is added or removed; the heat goes into breaking/forming intermolecular bonds:

q = mL

where L is the latent heat — of fusion (L_f, solid↔liquid) or vaporization (L_v, liquid↔gas). For water L_f ≈ 334 J/g and L_v ≈ 2260 J/g. On a heating curve, sloped segments use q = mcΔT and flat (plateau) segments use q = mL.

Biological context. Sweating cools the body through the large latent heat of vaporization of water — evaporating a small mass of sweat removes a large amount of heat.

Work in Thermodynamics

When a gas changes volume, it does work. On a PV diagram the work done by the gas equals the area under the process curve (no calculus needed for MCAT). For the common constant-pressure case:

W = PΔV = P(V₂ − V₁)

Special cases:

Isobaric (constant P): W = P·ΔV = P(V₂ − V₁).
Isochoric (constant V): W = 0 (no volume change).
Isothermal (constant T): W = nRT·ln(V₂/V₁).
Adiabatic (Q = 0): PV^γ = constant; W = (P₁V₁ − P₂V₂)/(γ − 1).

Sign convention: W > 0 when work is done by the gas (expansion); W < 0 when work is done on the gas (compression).

First Law of Thermodynamics

Statement: heat supplied to a system is used to increase the internal energy of the system and/or to do work by the system on its surroundings.

ΔU = Q − W

This is simply conservation of energy. Sign conventions:

Q > 0: heat added to the system; Q < 0: heat lost.
W > 0: work done by the system (expansion); W < 0: work done on the system.

First law in special processes

Thermodynamic processes — what's constant, what's zero
Process	Constant	Q	W (by gas)	ΔU	P-V relation
Isothermal	T	Q = W	nRT·ln(V₂/V₁)	0	PV = nRT (Boyle's law)
Isobaric	P	nC_pΔT	P·ΔV	nC_vΔT	V/T = const (Charles's)
Isochoric	V	nC_vΔT = ΔU	0	nC_vΔT	P/T = const (Gay-Lussac)
Adiabatic	Q = 0	0	(P₁V₁ − P₂V₂) / (γ − 1)	−W	PV^γ = const
Cyclic	Returns to start	Q = W (= area of loop on PV)	Net = area enclosed	0	Closed curve on PV diagram

Common trap. Different textbooks write the First Law as ΔU = Q − W (chemistry/physics convention W = work BY gas) or ΔU = Q + W (some chemistry books, W = work ON gas). Always check which convention is in use; the MCAT physics convention uses ΔU = Q − W.

Molar Specific Heat of Gas

For a gas, the heat needed to raise the temperature of 1 mole by 1 K depends on the path of heating. Two principal molar specific heats are defined:

C_v — molar specific heat at constant volume: Q_v = nC_vΔT. Since W = 0 in an isochoric process, all heat goes to raising U: ΔU = nC_vΔT.
C_p — molar specific heat at constant pressure: Q_p = nC_pΔT. The gas also does PΔV work, so more heat is required for the same ΔT: C_p > C_v always.

Values for ideal gases

Monatomic gas (He, Ar): C_v = (3/2)R, C_p = (5/2)R, γ = 5/3 ≈ 1.67.
Diatomic gas (O₂, N₂): C_v = (5/2)R, C_p = (7/2)R, γ = 7/5 = 1.40.
Polyatomic gas: C_v ≈ 3R, C_p ≈ 4R, γ ≈ 4/3.

Ratio γ = C_p/C_v appears in the adiabatic equation PV^γ = constant.

Relation Cp − Cv = R (Mayer's Relation)

For 1 mole of an ideal gas:

C_p − C_v = R

Where R = 8.314 J/(mol·K) is the universal gas constant. Derivation idea: at constant V, all the heat raises U; at constant P, the same ΔT also requires PΔV = RΔT of work to be done on the surroundings, so more heat is required.

Memory aid. "Pumping a tyre needs more heat than a sealed bottle." Constant-pressure heating requires extra energy to perform expansion work — that extra is exactly R per mole per kelvin.

Second Law & Entropy

The Second Law of Thermodynamics states that the total entropy of an isolated system never decreases; spontaneous processes increase the total entropy of the universe (ΔS_universe > 0). Heat flows spontaneously from hot to cold, never the reverse without work input.

Entropy (S) is a state function measuring the dispersal/disorder of energy (J/K). For a reversible transfer of heat at temperature T: ΔS = q_rev/T. Entropy increases with melting, vaporization, dissolving, and rising temperature.

Common trap. A living organism can decrease its local entropy (building ordered molecules) only by exporting even more entropy to its surroundings — the entropy of the universe still rises. The Second Law is never violated.

Heat engines

A heat engine takes in heat Q_h from a hot reservoir at T_h, converts part of it into work W, and dumps Q_c to a cold reservoir at T_c. Efficiency:

η = W/Q_h = 1 − Q_c/Q_h. The maximum (Carnot) efficiency is η_max = 1 − T_c/T_h, with temperatures in kelvin. No real engine can exceed Carnot efficiency — a consequence of the Second Law.

Heat Transfer Modes

Three modes of heat transfer
Mode	Mechanism	Medium	Example
Conduction	Direct molecular collisions transfer kinetic energy	Solids (esp. metals)	Heat through a metal spoon; body core to skin
Convection	Bulk movement of a heated fluid carries energy	Liquids and gases	Boiling water; blood circulation distributing body heat
Radiation	Emission of electromagnetic waves; no medium needed	Any (incl. vacuum)	Sun's heat; body heat lost as infrared

The body regulates temperature using all three, plus evaporation of sweat (latent heat). Radiated power rises steeply with absolute temperature (Stefan–Boltzmann, P ∝ T⁴).

Worked MCQs

Five MCQs that capture the high-yield testing patterns for this chapter.

Q1. A gas absorbs 500 J of heat and does 200 J of work. The change in its internal energy is:

700 J
300 J
500 J
−300 J

First Law: ΔU = Q − W = 500 − 200 = 300 J.

Q2. For an ideal monatomic gas, the molar specific heat at constant volume is:

R
(3/2)R
(5/2)R
(7/2)R

A monatomic gas has only translational degrees of freedom (3). Equipartition gives U = (3/2)nRT, so C_v = (3/2)R.

Q3. In an isothermal process applied to an ideal gas:

ΔU = Q
Q = W
Q = 0
W = 0

For an ideal gas U depends only on T, so isothermal means ΔU = 0 and the First Law gives Q = W.

Q4. Heat is added at a steady rate to a beaker of ice initially at 0°C. While the ice is melting, the temperature of the mixture:

Rises steadily
Stays constant at 0°C
Falls, then rises
Rises only after half the ice melts

During a phase change temperature is constant; the heat (q = mL_f) goes into breaking intermolecular bonds, not raising kinetic energy. Temperature rises only once all the ice has melted.

Q5. In an adiabatic process:

Q = 0 and ΔU = 0
Q = 0 and ΔU = −W
W = 0 and Q = ΔU
Q = −W and ΔU = 0

Adiabatic means no heat exchange (Q = 0). First Law ⇒ ΔU = −W. Adiabatic expansion cools the gas; adiabatic compression heats it.

Quick Recap

T(K) = T(°C) + 273.15; use kelvin in all gas-law/efficiency formulas.
Calorimetry: q = mcΔT (temperature change); q = mL (phase change, T constant).
First Law: ΔU = Q − W (W = work done BY gas); PV work = area under PV curve.
Isothermal: ΔU = 0; Isochoric: W = 0; Adiabatic: Q = 0; Cyclic: ΔU = 0.
C_v = (3/2)R (monatomic), (5/2)R (diatomic); C_p − C_v = R (Mayer's).
Second Law: ΔS_universe > 0 for spontaneous processes; heat flows hot → cold.
Carnot (max) efficiency η = 1 − T_c/T_h.
Heat transfer: conduction, convection, radiation.

Test yourself. Take a timed Thermodynamics quiz or browse all Physics MCQs to lock these concepts in.