D | Question 6 5 pts 4. When learning about heat capacity, we focused on using c

Question

D | Question 6 5 pts 4. When learning about heat capacity, we focused on using constant volume heat capacity Cvm or specific heat values (also constant volume) instead of constant pressure (isobaric) heat capacity Com-f water or a solid were the material being heated, then Cym or Com values are essentially identical. However, if a gas were the species being heated, the values are never equal b) (5 pts) In class, we discussed how using specific heat of water (184 J/(g K) or the constant volume heat capacity Cym(75.4 /(mol K) will lead to the exact same value of q. Show how the two values for water are related and then highlight how the two formulae differ when used correctly.

Explanation / Answer

4. In general specific heat(C) gives us an idea of the amount of energy(heat) we need to provide to a system in order to bring about a unit rise in the temperature of the system. It's value may vary depending on the process you are providing this energy. Hence we have two values of C namely Cv and Cp .

Cv for a gas is the change in internal energy (U) of a system with respect to change in temperature at a fixed volume of the system i.e. Cv =( U/ T)v  whereas Cp for a gas is the change in the enthalpy (H) of the system with respect to change in temperature at a fixed pressure of the system i.e Cp = ( H/ T)p.

We know that, H = U + PV (+ VP, P=0 for constant pressure) . So the enthalpy term is greater than the internal energy term because of the PV term i.e in case of a constant pressure process more energy is needed, to be provided to the system as compared to that of a constant volume process to achieve the same temperature rise, as some energy is utilized in the expansion work of the system. And the relation that correlates these two is Cp = Cv + R

But since liquids and solids can practically assumed to be incompressible, Cp and Cv for them have almost same values and hence only a single value of specific heat is used for them.

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