If carbon dioxide is cooled at 1 atm, it condenses directly...

If carbon dioxide is cooled at 1 atm, it condenses directly to a solid (dry ice) at $-78.4^{\circ} \mathrm{C}$. The heat of sublimation at this temperature is $\Delta \hat{H}_{\mathrm{sub}}\left(-78.4^{\circ} \mathrm{C}\right)=6030$ cal/mol. (a) Calculate the heat removal rate (kW) required to produce $300 \mathrm{kg} / \mathrm{h}$ of dry ice at 1 atm and $-78.4^{\circ} \mathrm{C}$ if $\mathrm{CO}_{2}(\mathrm{v})$ at $20^{\circ} \mathrm{C}$ is the feed. (b) Suppose the process is carried out at 9.9 atm instead of 1 atm with the same initial and final temperatures. Referring to Figure $6.1-1 b,$ write an expression for the required heat removal rate in terms of heat capacities and latent heats of $\mathrm{CO}_{2}$ in different phases.

If carbon dioxide is cooled at 1 atm, it condenses directly to a solid (dry ice) at $-78.4^{\circ} \mathrm{C}$. The heat of sublimation at this temperature is $\Delta \hat{H}_{\mathrm{sub}}\left(-78.4^{\circ} \mathrm{C}\right)=6030$ cal/mol.
(a) Calculate the heat removal rate (kW) required to produce $300 \mathrm{kg} / \mathrm{h}$ of dry ice at 1 atm and $-78.4^{\circ} \mathrm{C}$ if $\mathrm{CO}_{2}(\mathrm{v})$ at $20^{\circ} \mathrm{C}$ is the feed.
(b) Suppose the process is carried out at 9.9 atm instead of 1 atm with the same initial and final temperatures. Referring to Figure $6.1-1 b,$ write an expression for the required heat removal rate in terms of heat capacities and latent heats of $\mathrm{CO}_{2}$ in different phases.

Key Concepts

Pressure Effects on Phase Equilibria

Pressure significantly influences phase change behavior and equilibrium conditions. Altering the pressure can shift the temperatures at which phase transitions occur and modify the latent heat and heat capacity values relevant to each phase. Understanding these pressure effects is essential when formulating expressions for heat removal rates, particularly when comparing processes at different pressures with the same initial and final temperatures.

Energy Balance in Cooling Processes

This key concept involves accounting for all energy changes in a system undergoing cooling. In the context of phase change, the energy balance includes both the removal of sensible heat (to lower the temperature) and latent heat (to complete the phase transition). Accurately determining the overall heat removal rate requires integrating these energy contributions over time and mass flows.

Latent Heat of Sublimation

Latent heat is the energy required to accomplish a phase change at a constant temperature and pressure. For sublimation, in particular, this is the energy needed to convert a substance directly from the solid phase to the gas phase (or vice versa during deposition). This parameter is essential for calculating the energy changes in processes where no intermediate liquid phase is involved, and it directly affects the amount of heat removal needed during cooling.

Phase Transition Thermodynamics

This concept deals with the study of changes of state, such as the transition between gas and solid. Understanding phase transitions involves analyzing the energy changes and conditions (temperature and pressure) at which a substance undergoes a change in state without passing through an intermediate phase. In problems involving direct condensation to a solid (sublimation/deposition), it is crucial to know the conditions under which these transitions occur.

Heat Capacities and Sensible Heat

Heat capacity is a measure of the amount of heat required to change a substance's temperature by a certain amount. Sensible heat refers to the energy exchanged that results in a change in temperature, as opposed to latent heat which causes a phase change at a constant temperature. When cooling a feed material, the sensible heat removed before a phase transition is as critical as the latent heat associated with the transition itself.

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