Chemical Thermodynamics: Heat Capacity - Constant Pressure or Volume

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Frances Docherty

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Frances Docherty 4 weeks, 1 day ago

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Frances Docherty 4 weeks, 1 day ago

Created this as a copy of Heat Capacity - Constant Pressure or Volume.

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The following reaction takes place in an open beaker:

$\mathrm{NaOH + HCl → H_2O + NaCl}$ .

The reaction causes the temperature of the solution to change by $\mathrm{ΔT}$ . Is the change in temperature dependent on $\mathrm{C_p}$ or $\mathrm{C_v}$ or neither?

Gap 0.

An similar reaction in the gaseous phase takes place in a sealed, rigid, completely filled vessel, causing the temperature of the solution to change by another $\mathrm{ΔT}$ . Is this change in temperature dependent on $\mathrm{C_p}$ or $\mathrm{C_v}$ or neither?

Gap 1.

If another reaction took place in the gaseous phase within a sealed vessel with an adjustable lid height, upon which a piston pushed down during the reaction, would the change in temperature be dependent on $\mathrm{C_p}$ or $\mathrm{C_v}$ or neither?

Gap 2.

Advice

When considering the temperature increases of substances and solutions during chemical and physical changes, we must choose which heat capacity to use.

If our system maintains a constant volume during the process, we use the heat capacity at constant volume, $\mathrm{C_v}$ ; if it maintains a constant pressure, we use the heat capacity at constant pressure, $\mathrm{C_p}$ . If both the volume and pressure of the system change during the process for which we want to calculate the temperature change, then neither $\mathrm{C_v}$ or $\mathrm{C_p}$ are applicable, and the heat capacity we use will take on a third value, more difficult to calculate (you will not have to worry about this third case when calculating temperature changes, unless you are explicitly provided this alternate heat capacity).

We are asked to determine the most appropriate heat capacity to be used in each of three scenarios involving a solution being heated.

In the first case, the solution heats up in an open beaker. This means the solution will be free to expand, and thus will not have a constant volume. However, the atmospheric pressure of the surroundings will remain virtually unaffected by the process within the beaker, so the pressure acting down on the solution will remain constant. Thus, in this case we use $\mathrm{C_p}$ .

In the second case, a gas mixture heats up within a sealed, rigid vessel. This means the mixture will not be free to change its volume beyond the vessel's constraints, and so as the vessel is already completely filled, the volume cannot change during the process. The pressure, however, will change as the reaction progresses, as when the pressure of the reacting mixture (acting on the vessel walls) changes when the solution tried to expand, there will be a proportional change in the pressure acting back on the mixture from the vessel walls. Thus, in this case we use $\mathrm{C_v}$ .

In the third and final case, a gas mixture is in a sealed vessel in which its pressure will change (for the same reasons outlined previously), but the moving piston changing the volume of the vessel will also mean that the mixture cannot maintain a constant volume. Thus, in this case we cannot use either $\mathrm{C_p}$ or $\mathrm{C_v}$ . If you are asked to use a heat capacity value in a calculation for such a situation, you should expect to be provided an alternate value for $\mathrm{C}$ .

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Chemical Thermodynamics: Heat Capacity - Constant Pressure or Volume

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Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

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