Thermodynamics and Energy Changes (5E) - Chem & Physics

1. State the definition of entropy change for a reversible process.

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

2. For an adiabatic process, what is the heat transfer $q$?

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

3. At constant $T$ and $P$, what sign of $\Delta G$ indicates a spontaneous process?

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

4. State the definition of enthalpy in terms of $U$, $P$, and $V$.

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

5. What is the formula for heat absorbed at constant pressure for a temperature change $\Delta T$?

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

6. Find $\Delta U$ if $q=-50\,\text{J}$ and $w=+20\,\text{J}$ for the system.

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

7. Find $q_p$ if $n=2$ and $C_p=30\,\text{J·mol}^{-1}\text{·K}^{-1}$ for $\Delta T=10\,\text{K}$.

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

8. What is the sign convention for $w$ when the system does work on the surroundings?

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

9. Which sign of $\Delta H$ indicates an exothermic reaction at constant pressure?

   $\Delta H<0$. Exothermic reactions release heat, corresponding to a decrease in the system's enthalpy.

10. What is the relationship between $\Delta G^\circ$ and the equilibrium constant $K$?

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

11. What is the sign convention for $q$ when heat enters the system?

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

12. What is the relationship between $C_p$ and $C_v$ for an ideal gas?

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

13. State the Gibbs free energy equation relating $\Delta G$, $\Delta H$, $T$, and $\Delta S$.

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

14. State Hess's law for combining reaction enthalpies.

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

15. What is the relationship between $\Delta U$ and $q$ at constant volume?

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

16. Find $\Delta G$ at $T=300\,\text{K}$ if $\Delta H=20\,\text{kJ}$ and $\Delta S=50\,\text{J·K}^{-1}$.

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

17. State the ideal gas law relating $P$, $V$, $n$, and $T$.

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

18. State the first law of thermodynamics using $\Delta U$, $q$, and $w$.

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

19. Find $w$ if $P_{\text{ext}}=2\,\text{atm}$ and the system expands by $\Delta V=3\,\text{L}$.

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

20. What is the relationship between $\Delta H$ and $q$ at constant pressure (PV work only)?

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

21. What is the criterion for spontaneity in terms of the universe entropy change?

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

22. What is the formula for pressure–volume work at constant external pressure?

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

23. For an isochoric process, what is the work $w$?

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

24. What is the formula for heat absorbed at constant volume for a temperature change $\Delta T$?

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

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