Question

Volumetric expansion coefficients of simple materials are often well cataloged. However, the thermal expansion coefficient ?β of a human body is less well known. This could affect the human body's specific gravity and, therefore, measurements of its body‑fat ratio.

Suppose that a human body of weight ?0w0 on dry land is placed on a scale while completely immersed in formaldehyde of temperature ?1.T1. Once the temperature increases by Δ?,ΔT, the scale reading drops by Δ?.Δw.

Derive an expression for ?β in terms of Δ?,ΔT, ?0,w0, and Δ?Δw by assuming that the ratio of the density of formaldehyde ?fρf and the initial density of the body ?bρb is ?=?f/?b.R=ρf/ρb. Assume also that ?fρf does not change when heated.

?=β=

If the body weighs 159.8 lb159.8 lb on dry land and his weight reading lowers by 0.237 lb0.237 lb when the formaldehyde is heated from 63.40 °F63.40 °F to 82.80 °F,82.80 °F, calculate the coefficient of volume expansion of the body.* Assume ?=0.850R=0.850.

?=β=

1/°C1/°C

* The coefficient ?β will likely vary widely from one human body to the next. The numerical value computed in this example should not be considered factual.

Answer 1