Energy Balance
Closed Systems

Upon studying this section, you should be familiar with the following:

Energy Balances for Closed Systems


Energy balances on closed systems is the first type of energy balances introduced in this course. However, since most chemical processes involve in and out streams, closed energy balances are not used as frequently as open system energy balances. Nevertheless, they should be understood, and if asked, you should be able to perform them. Closed systems include batch reactors, classic piston in a cylinder assemblies, and storage tanks.

Closed System Energy Balance Equation:

ΔU + ΔEk + ΔEp = Q + W

ΔU = 0 if there are no temperature changes, phase changes, or chemical reactions.
In general, ΔU is also 0 when small pressure changes occur as well (a few atm).

ΔEk = 0 if the system doesn't accelerate

ΔEp = 0 if the system doesn't change in height

Q = 0 if the system doesn't exchange heat with the surroundings, that is, if the system is adiabatic or insulated

W = 0 if the system has no moving boundry (ex. piston), or if there are no moving parts, electrical current, or radiation exchange with the system and the surroundings.

Example 1:

40 kg of water initially at 25 oC is contained in a perfectly insulated steel tank that weighs 5 kg. A steel ball that weighs 3 kg with an initial temperature of 500 oC is immersed into the water before the system is allowed to reach a final temperature (until equilibrium). CV,water = 4.18 and CV,steel = .5 kJ/(kg*K). What is the final temperature?

Comment: This is an interesting problem, I remember solving it (hot metal immersed in water), in several classes, and on several tests, such as, 1st semester freshmen (general) chemistry, first semester physical chemistry, intro to chemical engeering, and first semester thermodynamics, (if you had chemistry in high school, you may have seen it there, too.)

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