Thermodynamics and Energy Changes (5E) - MCAT Chemical and Physical Foundations of Biological Systems

$q>0$. In thermodynamic conventions, heat absorbed by the system from surroundings is assigned a positive value.

$w<0$. Work performed by the system on surroundings reduces the system's energy, thus assigned a negative sign.

$\Delta U=q+w$. The first law states that internal energy change equals heat added to the system plus work done on the system.

$w=-P_{\text{ext}}\Delta V$. For irreversible expansion at constant external pressure, work equals the negative product of pressure and volume change.

$w=0$. Isochoric processes involve no volume change, hence no pressure-volume work is performed.

$q=0$. Adiabatic processes, by definition, prohibit heat exchange between the system and surroundings.

$\Delta H=q_p$. Enthalpy change equals heat transferred at constant pressure when only PV work occurs.

$\Delta U=q_v$. At constant volume, internal energy change equals heat transferred since no work is done.

$H=U+PV$. Enthalpy accounts for internal energy plus the energy associated with pressure-volume work.

$PV=nRT$. The ideal gas law describes the proportional relationship between pressure, volume, moles, and temperature.

$q_p=nC_p\Delta T$. Heat capacity at constant pressure quantifies energy required to raise temperature for a given amount of substance.

$q_v=nC_v\Delta T$. Heat capacity at constant volume measures energy input for temperature change without volume alteration.

$\Delta H_{\text{net}}=\sum \Delta H_{\text{steps}}$. Since enthalpy is a state function, the net change equals the sum of stepwise changes regardless of path.

$\Delta S=\frac{q_{\text{rev}}}{T}$. For reversible processes at constant temperature, entropy change is reversible heat divided by temperature.

Spontaneous if $\Delta S_{\text{univ}}>0$. The second law dictates that spontaneous processes increase the total entropy of the universe.

$\Delta G=\Delta H-T\Delta S$. Gibbs free energy combines enthalpy and entropy to assess spontaneity at constant temperature and pressure.

$\Delta G<0$. Negative Gibbs free energy change indicates the process can occur spontaneously under those conditions.

$\Delta G^\circ=-RT\ln K$. This equation links thermodynamic favorability under standard conditions to the equilibrium position.

$\Delta U=-30,\text{J}$. The first law calculates internal energy change as the sum of heat and work with proper signs.

$w=-6,\text{L·atm}$. Expansion work against constant pressure is negative the product of pressure and volume increase.

$q_p=600,\text{J}$. Constant pressure heat transfer uses molar heat capacity to relate energy to temperature change.

$\Delta G=5,\text{kJ}$. Gibbs free energy subtracts the entropy term from enthalpy, ensuring unit consistency in calculations.

$C_p=C_v+R$. The difference arises from the additional work term at constant pressure for ideal gases.