Summary:

The amount of heat (dq) transferred from the surroundings to a unit mass at a constant volume equals the specific internal energy increase

(du=dq| _V=const ),

while the heat transfer at a constant pressure increases enthalpy

(dh=dq| _p=const).

Supplied heat increases temperature du=c_v.dT, dh=c_p.dT, with the exception of phase changes, where latent heat of vaporisation (dh_LG=r_LG), heat of fusion (dh_SL=r_SL) or heat of sublimation (dh_SG=r_SG) are added at T=const. Liquids and solids are nearly incompressible, so that we need not consider mechanical work in energy balances (in this case the specific heat capacities are equal c _p =c _v and the relation between the amount of heat transferred to a body and the temperature increase is q=c _v T=c _p T ). When mechanical work cannot be neglected (compressible substances, usually gases) cp is greater than cv and the more general definition of enthalpy

h=u+pv must be used.

Some phase equilibrium phenomena accompanied by heat transfer have been described qualitatively (boiling, melting and sublimation) and the two simple empirical relationships between temperature of boiling and pressure have been presented:

T=100 p^1/4

for water (we can extend this simple power-law model for other liquids, too,

T/T_c=(p/p_c)^m ,

where Tc is critical temperature, pc is critical pressure and the exponent m can be calculated from the boiling point temperature at atmospheric pressure). More accurate is the

Antoine equation ln p = A-B/(T+C),

parameters A,B,C are presented in Tab. 7.1, or in Šesták (1981).

Heat released or consumed by a chemical reaction can be evaluated according to Hess's law from the tabulated enthalpies of formation (D^f)₂₉₈. The actual reaction is replaced by hypothetical reactions describing decomposition of reagents to free elements (at the most stable state, e.g., C, S, O2, H2,...) and by subsequent formation of products from these free elements. The enthalpy of formation equals the enthalpy of decomposition (with the opposite sign) and thus the reaction heat is the difference between the enthalpies of formation of products and reactants. This difference can be calculated as the sum of enthalpies of formation of all species involved in the reaction using stoichiometric coefficients as DH=åjiDhf (remember: stoichiometric coefficients of reactants are negative).
The first law of thermodynamics expresses the principle of energy conservation, stating that the amount of heat transferred to a closed system (dQ) equals the sum of the internal energy increase (dU) plus volumetric mechanical work (p.dV) done by the system

dQ=dU+p.dV

(the symbol dQ emphasises the fact that heat Q is not a state variable and its change dQ is not a unique function of ending states). Remark: For other forms of work the more general formulation has to be used: dQ=dU+p.dV+s.dA+U(e).dQ(e), where s.dA is the mechanical work done by the change of surface dA (s is the surface stress) and U(e).dQ(e) is electrical work corresponding to transfer of electrical charge dQ(e) between electrical potential U(e).

The second law of thermodynamics states that entropy S, a measure of the spontaneity of processes, always increases in a closed, thermally insulated system. Change of entropy can be computed by integration of

dS=(dQ/T)_rev

, where dQ is heat transferred to the system in a reversible way. Generally dS=dQ/T+dS_irrev, where dQ is the actual amount of heat transferred across the boundary of the system, and dSirrev is the part of the entropy change caused by irreversible processes inside the system. The spontaneity of the processes taking place in a system at constant temperature and pressure (e.g., at phase changes) can be more comfortably evaluated from

Gibbs energy defined as G=H-TS.

Spontaneous processes are characterised by decreasing Gibbs energy G (note the negative sign in the definition G » -S). The negative value of the Gibbs energy change dG of a transformation A>B (a reaction, phase change,etc.) means that the transformation A>B is more probable than B>A. Thus dG=0 is a condition describing, e.g., the equilibrium of chemical reactions. Similarly, Helmholtz energy, used to express equilibrium at constant pressure and volume is defined as F=U-TS. The conditions V,p=const are not so frequently encountered in engineering practice, and for this reason we pay little attention to F.
These three thermodynamic functions (S-entropy, G-Gibbs energy, F- Helmholtz energy) have the same meaning, i.e., their changes characterise spontaneity of processes under different external conditions, see the following table:

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