Important Concepts in Chapter 19 (First Law of Thermodynamics)

A comprehensive set of practice flashcards covering state properties, sign conventions, first law, adiabatic/isothermal processes, enthalpy, heat capacities, Hess's Law, standard formation enthalpies, and the ideal-gas equation of state.

What is a state property and how is ΔX defined for a state property?

A state property depends only on the state of the system, not its history. ΔX = Xfinal − Xinitial for a state property.

Differentiate between extensive and intrinsic state properties with examples.

Extensive properties scale with the amount of substance (e.g., volume, energy, mass). Intrinsic properties do not depend on amount (e.g., density, pressure, temperature, concentration).

What is the difference between exothermic and endothermic processes?

Exothermic processes release heat to the surroundings; endothermic processes absorb heat from the surroundings.

What is the sign convention for heat flow in thermodynamics?

q is positive when heat flows into the system from the surroundings and negative when heat flows out of the system to the surroundings.

What is the sign convention for work in thermodynamics?

w is positive when work is done on the system and negative when work is done by the system.

What is the expression for work in terms of external pressure for a quasi-static process?

w = - ∫ P_ext dV

What defines a reversible process?

A reversible process is one where the system and surroundings can be returned to their original states by exactly reversing the process; it is an ideal process with infinitesimally small changes.

In a reversible process, how is wr related to pressure and volume?

wr = - ∫ P dV, where P is the system pressure.

Is internal energy a state function? Why or why not?

Yes. Internal energy is a state function; heat and work depend on the path between states.

What is the differential form of the first law of thermodynamics?

dU = δq + δw, or equivalently ΔU = q + w.

What is an adiabatic process?

An adiabatic process has no heat transfer: q = 0 and δq = 0.

What is the adiabatic relation for an ideal gas in terms of P and V?

PV^γ = constant, where γ = Cp/Cv (e.g., γ = 5/3 for monoatomic, γ = 7/5 for diatomic).

What is the relation between T and V in an adiabatic process?

T V^{γ-1} = constant; equivalently T2/T1 = (V1/V2)^{γ-1} and P2/P1 = (V1/V2)^γ.

What are the heat capacity ratio values γ for monoatomic and diatomic ideal gases?

γmonoatomic = 5/3; γdiatomic = 7/5.

What is the isothermal relation for an ideal gas?

For an isothermal process, T is constant and PV = nRT, so P1V1 = P2V2.

What is enthalpy and how is it related to internal energy?

Enthalpy H = U + PV.

At constant pressure, how does ∆H relate to ∆U and ∆V?

∆H = ∆U + P∆V.

From calorimetry, what can be determined at constant volume and at constant pressure?

At constant volume, ∆U = qV; at constant pressure, ∆H = qP.

In reactions involving ideal gases at constant temperature and pressure, how is ∆H related to ∆U and ∆n_g?

∆H = ∆U + RT ∆ng, where ∆ng is the change in moles of gas.

What are Cv and Cp definitions and their relation to q?

Cv = (∂U/∂T)V ≈ ΔU/ΔT = qV/ΔT; Cp = (∂H/∂T)P ≈ ΔH/ΔT = qP/ΔT.

What is the relation between Cp and Cv for an ideal gas and typical Cv values for monoatomic and diatomic gases?

Cp − Cv = R for an ideal gas. For a mole: Cv(monoatomic) = 3R/2; Cv(diatomic) = 5R/2 (per mole).

How is enthalpy change with temperature related to Cp when no phase transitions occur?

ΔH(T2) − ΔH(T1) = ∫{T1}^{T2} Cp(T) dT. From 0 K: H(T) − H(0) = ∫{0}^{T} Cp(T) dT.

What additional term appears in ΔH when there is a phase transition at T3?

A latent heat term at the phase transition is added: H(T) − H(0) = ∫{0}^{T3} Cpphase1 dT + ΔHphasetransition + ∫{T3}^{T} Cpphase2 dT.

What is Hess's Law in terms of enthalpy?

Enthalpy changes for chemical reactions are additive.

What does ΔrH° represent?

Standard reaction enthalpy for a reaction at standard states (per mole of a specified reagent).

What is the standard molar enthalpy of formation ΔfH°?

Standard enthalpy of formation: enthalpy change for forming one mole of a substance from its elements in their standard states.

What is ΔfH° for elements in their standard state?

Zero.

How can you calculate ΔHr(T2) from ΔHr(T1) using Cp values?

ΔHr(T2) = ΔHr(T1) + ∫_{T1}^{T2} ΔCp(T) dT, where ΔCp(T) = Cp,products − Cp,reactants.

What is the standard-state condition that makes ΔfH° = 0 for Br2?

Br2 is 0 in its standard state when it is liquid at 298 K and 1 bar; Br2(g) would not be zero.

What is the equation of state for an ideal gas?

PV = nRT (ideal gas law).