Does the rate of pressure build up keep increasing or remain constant when a liquid is heated in a closed container?

Question

Consider a scenario where we are heating a liquid partially filled, in a closed vessel. Assume that we are supplying the thermal energy at a constant rate (which is quite high enough) to the vessel and that the vessel loses minimal heat to surrounding. Then does the rate at which pressure builds up within the vessel remain constant or will it change with time.

Note: There isn't heat being directly transferred to the gases above the liquid surface within the container, from the heat source at any point of time.

I hope I haven't missed any Caveats to answer the question properly.

Answer 1

The pressure increases with heating.

The relevant model here includes the activity and the chemical potential or partial molar Gibbs free energy, which is equal for phases at equilibrium, which we'll assume in this answer.

The relationship between the chemical potential and activity is

$$\mu=\mu_0+RT\ln a,$$

where the activity is 1 for a pure solid and liquid and is the fugacity (or the pressure for an ideal gas) for a gas. Therefore, assuming an ideal gas,

$$\mu_{0,\text{L}}=\mu_{0,\text{G}}+RT \ln\frac{p}{p_0},$$

where $\text{L}$ and $\text{G}$ indicate liquid and gas, respectively, and $p_0$ is atmospheric pressure to remove the units from the logarithm.

The outcome is an exponential increase in pressure in an enclosed liquid–vapor system with increasing temperature. At some point the critical threshold is exceeded and the system is filled with a supercritical fluid.

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