Basic Thermodynamics ~ J. Pohl © www.THERMOspokenhere.com (D116) -  (D117)

Chef Thickens the Soup

A pot on a range containing four liters of soup is at a gentle boil. The chef intends to thickened the soup, slowly, by boiling away 30% of its water. The stove heating element is rated at 1800 Watts.
Estimate the Least Time of heating is required to thicken the soup?

Solution:  We select the 4 liters of water as a closed system, Fig 1. Initially the water is boiling. It continues to boil until 30% is changed to vapor. Although good soup is not water, we approximate the soup to be (or to have the properties of) pure water. As water heats to vapor it disperses into the kitchen.

Event: The kitchen is at atmospheric pressure, hence the heat of the "thickening" process occurs at the constant pressure of the surrounding atmosphere.

Upon boiling the water (initally) and water plus vapor (finally) experience near zero changes of kinetic or potential energies. However the boiled water will experience a change of volume. Work happens by virtue of the expansion of part of the water - as it becomes vapor at one atmosphere. This type event is called a "batch process." The event "commences" and at a later time attains its second conditions.

A basic energy equation, written in rate-form is :

(1)e01

Equation (1) is written to indicate a summation of works and a summation of heats. These notations remind us to address theis terms carefully.

(2)

Eqn (2) above but with summations.

ΣWorks is expanded. Every substance has the "simple compressaible" work possibility. Ocassionally there are "other" mdes relevant; but not in this case. ΣHeats is expanded. Heat from the range is expected. There will also be heat from the soup to the surroinding kitchen air. Since we are unable to calculate this heat (at this level of study) we must assume it is small or zero (/). This decision cast out answer as a "least" time of the event.

(3)

Inserting these definitions, we realize kinetic and potential energies (left-of-equality) and any work related thereto equal zero. KE, PE and their works are insigmificant, consequently struck from the equation.

The significance of work-rate upon a compressible as it experiences phase change

(4)

4

bbh

(5)

8

VVVVVVV

(6)

6

XXXX

(7)


Text

Students of thermodynamics might believe there are thousands of equations. There are not that many, but it might seem so because there are three mathematical forms of Newton's 2nd Law, the mass, momentum, and energy equations. These are the differential form, rate form and increment form. Of course the forms are equavalent. There are mathematical operations whereby each form can be transformed to either of the other two. Logically, a student might ask, "Is one of the forms superor to the two and ifso, why so?"

To proceed we must cast each enthalpy, H, in terms of its mass and its specific enthalpy mh. The initial state is saturated liquid at one atmosphere. In the final state, some water remains as saturated liquid and some has "boiled-off" as saturated vapor. The subscripts " f " and " g " are used for the saturated liquid and vapor states, respectively.

Some algebra will provide H2 - H1:

(4)4
(5)5

Thirty percent of the original mass of saturated liquid is heated to become vapor. Thus the mass of vapor generated is:

mg,2 = 0.30 [4000 cm3(1 g/cm3] = 1200 grams. (6)6

The enthalpy of phase change (some call this "latent heat of boiling") is:

hg - hf = (2675 - 419) J/g (7)7

Entering these numbers we obtain the "least" time required.

(8)8

Thermodynamic calculations do not provide correct answers. Approximate answers are obtained. In this case this time is the least because we realize some of the heat of the cooking range will pass to the surroundings.

Chef Thickens the Soup

A pot on a range contains four liters of soup and is at a gentle boil. The chef intends that the soup be thickened slowly by boiling away 30% of its water. The rating of the stove element is 1800 watts.

What is the least time required to thicken the soup?