Important Concepts in Chapter 19 (First Law of Thermodynamics)

Flashcards covering key concepts and equations from the First Law of Thermodynamics notes.

What is a state property?

A property that depends only on the current state of the system, not its history (e.g., volume, energy). For a state property X, ΔX = Xfinal − Xinitial.

Differentiate extensive and intrinsic (state) properties

Extensive properties are proportional to the amount of substance (e.g., volume, energy, mass); intrinsic (intensive) properties are independent of amount (e.g., density, pressure, temperature, concentration).

Define exothermic and endothermic processes

Exothermic: a process that releases heat to the surroundings. Endothermic: a process that absorbs heat from the surroundings.

Sign convention for heat

q is positive when heat flows from the surroundings to the system; q is negative when heat flows from the system to the surroundings.

Sign convention for work

w is positive if work is done on the system; w is negative if work is done by the system.

Equation for work with external pressure

Work is w = - ∫ Pext dV, where Pext is the external pressure.

What is a reversible process?

An ideal process in which the system and surroundings can be returned to their original states by exactly reversing the process; changes are infinitesimally small.

Reversible process relation for work

For a reversible process, w_r = - ∫ P dV, where P is the system pressure.

Is internal energy a state function? Are heat and work path dependent?

Internal energy U is a state function; heat q and work w are path dependent.

First law of thermodynamics (differential form)

dU = δq + δw; equivalently ΔU = q + w.

Adiabatic process

No heat transfer to or from the system; q = 0 (δq = 0).

Adiabatic relations for an ideal gas

For an ideal gas in an adiabatic process: TV^(γ−1) = constant and PV^γ = constant, where γ = Cp/Cv. For monoatomic γ ≈ 5/3; for diatomic γ ≈ 7/5.

Isothermal process for an ideal gas

Temperature is constant; P1V1 = P2V2.

Enthalpy

H = U + PV.

Constant-pressure enthalpy change

At constant pressure, ΔH = ΔU + PΔV.

Relating qV and qP to U and H

Experimentally, qV = ΔU (constant volume) and qP = ΔH (constant pressure).

Reaction enthalpy for ideal gases at constant T and P

ΔH = ΔU + RT Δng, where Δng is the change in moles of gas.

Heat capacity at constant volume

Cv = (∂U/∂T)_V ≈ ΔU/ΔT.

Heat capacity at constant pressure

Cp = (∂H/∂T)_P ≈ ΔH/ΔT.

Cp − Cv for an ideal gas

Cp − Cv = nR.

Cv values for monoatomic and diatomic ideal gases

Monoatomic: Cv = (3/2) nR. Diatomic: Cv = (5/2) nR (at moderate temperatures, ignoring vibrational modes).

Enthalpy temperature dependence for nonphase-changing systems

If no phase transition between 0 K and T, H(T) − H(0) = ∫0^T CP(T') dT'. If a phase transition occurs at T3, the integral splits with CP during each phase plus latent heat.

Enthalpy change across a phase transition

If a phase transition occurs at T3, H(T) − H(0) = ∫0^T3 CPphase1(T)dT + ΔPTH + ∫T3^T CPphase2(T)dT.

Standard reaction enthalpy

ΔrH° is the enthalpy change for a reaction under standard states, per mole of reaction.

Standard molar enthalpy of formation

ΔfH° is the standard enthalpy change for forming one mole of a substance from its elements in their standard states.

Enthalpy of elements in standard state

ΔfH° for elements in their standard state is zero (e.g., Br2(l) = 0 at 298 K and 1 bar; Br2(g) is not zero).

Temperature dependence of reaction enthalpy

ΔrH(T2) = ΔrH(T1) + ∫T1^T2 ΔCp(T) dT, where ΔCp(T) = Cp,products − Cp,reactants.

Example: ΔrH(T2) for aA + bB → cC + dD

ΔrH(T2) = ΔrH(T1) + ∫T1^T2 ΔCp(T) dT, with ΔCp(T) = c Cp,C + d Cp,D − a Cp,A − b Cp,B.

Hess's law

Enthalpy changes for a chemical process are additive; the total ΔH is the sum of the enthalpy changes along any pathway.

Standard states for elements and zero enthalpy formation

The standard enthalpy of formation of elements in their standard state is zero; there can be exceptions when phase is different.

Chemical reaction enthalpy sign convention

ΔHr is + for endothermic (heat absorbed) and − for exothermic (heat released).

Reaction enthalpy for formation from elements

ΔfH° is the standard enthalpy of formation for forming one mole of a compound from its elements.

Ideal gas equation of state

For an ideal gas, PV = nRT (no interparticle interactions; holds in the dilute limit).

Internal energy and enthalpy are state functions, but heat and work are path-dependent. T or F?

True

Extensive properties do not depend on the amount of substance present. T or F?

False

Pressure, temperature, and density are intrinsic (intensive) properties. T or F?

True

Volume and mass are examples of extensive properties. T or F?

True

If X is a state function, the change in X depends on the path between two states. T or F?

False

Heat is positive when it flows from the surroundings into the system. T or F?

True

T/F: Work is positive when done on the system.

True

T/F: Expansion work done by the system is considered negative.

True

T/F: Work is given by w = −PextΔV for expansion/compression.

True.

T/F: Work and heat are state functions.

False.

T/F: In a reversible process, the system can be returned to its original state without leaving any net change in the surroundings.

True.

T/F: Reversible processes occur infinitely slowly and are idealized.

True.

T/F: Internal energy is path dependent because it changes with the process taken.

False.

T/F: The First Law of Thermodynamics states ΔU=q+w.

True

T/F: The First Law allows creation of energy from nothing if work is negative.

False.

T/F: For an ideal gas in an isothermal process, ΔU=0 and q=−wq

True.

T/F: In an adiabatic process, q=0 but ΔU=w.

True.

T/F: Isothermal expansion of an ideal gas results in no work being done.

False.

T/F: For an isothermal process, P1​V1​=P2​V2​.

True.

T/F: In an adiabatic process, temperature remains constant.

False.

T/F: Enthalpy is defined as H=U+PV

True.

T/F: At constant pressure, qp=ΔH

True.

T/F: CP−CV=nR for an ideal gas.

True.

T/F: For a monatomic ideal gas, CV=3nR/2

True.

T/F: For a diatomic ideal gas with no vibrational modes excited, CV​=7nR/2.

False.

T/F: Hess’s Law states that the enthalpy change of a reaction is independent of the path taken.

True.

T/F: Standard enthalpy of formation of elements in their standard state is zero.

True.

T/F: Standard enthalpy of formation of Br2 ​(g) at 298 K is zero.

False.

T/F: Enthalpy changes for chemical reactions are additive.

True.

T/F: An exothermic reaction has a positive ΔH

False.