Geometric Model by Richard P. Baker, Thermodynamic Surface for Water, Ice, and Steam, Baker #253


In the 1870s physicists in Scotland and the United States began to make three-dimensional models of the thermal properties of matter. The height of this wire surface corresponds to the volume of ice, water and steam as this changes with pressure (pressure increases coming toward the front of the model) and temperature (temperature increases going to the right). The solid state – with relatively slow changes in volume with temperature and pressure, and low temperatures - is represented by the relatively flat surface on the left. The part of the board under it is marked S. When ice melts, the volume decreases until melting is complete. Water expands more rapidly with temperature than ice, so that the surface rises more rapidly from the middle of the front going right. The part of the board under this section of the surface is marked L. As temperature rises, water turns to steam, and the volume increases even more rapidly. The section of the board under this part of the surface is marked V for vapor.

A paper sticker glued to the underside of the base reads: No. 253 (/) Water Steam and Ice.

This is one of a series of nine models Baker made that relate to thermodynamic surfaces. It was designed during his years at the University of Iowa under the supervision of his German-born colleague Karl Eugen Guthe (1866–1915), who taught in the physics department there from 1905 until 1909. Baker’s correspondence indicates that copies of the model were purchased by Columbia University and by the University of Michigan. The model remained in Baker’s catalog as late as 1931. A card catalog in the Baker papers indicates that the model sold at one time for $7.50.

This particular example of the model was on loan for exhibition at MIT from 1939 until the mid-1950s. It, along with the other models in accession 211257, came to the Smithsonian from MIT in 1956.


Accession file 211257.

J. Willard Gibbs, “A Method Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces,” Transactions of the Connecticut Academy, 2, 1873, pp. 382–404. Gibbs refers to earlier work of the Scottish engineer James Thomson, who devised a surface for representing the pressure volume and temperature of carbonic acid and carbon dioxide.

H. Randall to Baker, January 15, 1908 and Columbia University to Baker, August 6, 1918, Richard P. Baker Papers, University Archives, University of Iowa, Iowa City, Iowa.

Richard P. Baker, Mathematical Models, Iowa City, 1931, p. 18.

Date Made: ca 1905-1935

Maker: Baker, Richard P.

Location: Currently not on view

Place Made: United States: Iowa, Iowa City

Subject: Mathematics


See more items in: Medicine and Science: Mathematics, Science & Mathematics, Mathematical Association of America Objects


Exhibition Location:

Related Publication: Baker, Richard P.. Mathematical Models

Credit Line: Gift of Frances E. Baker

Data Source: National Museum of American History

Id Number: MA.211257.045Accession Number: 211257Catalog Number: 211257.045

Object Name: geometric model

Physical Description: wood (overall material)metal (overall material)red (overall color)white (overall color)blue (overall color)black (overall color)soldered and bolted (overall production method/technique)Measurements: average spatial: 31.2 cm x 31.1 cm x 23.9 cm; 12 9/32 in x 12 1/4 in x 9 13/32 in


Record Id: nmah_1082212

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