Gough-Joule effect

As Gough Joule effect [ ɡɒf dʒuːl ] is in the original sense, the phenomenon indicates that under mechanical tension standing elastomers (such as. For example, rubber ) to contract when heated, rather than to other body extend . The effect is after John Gough , who first observed it in 1802, and James Prescott Joulewho systematically examined it in the 1850s. If the elastomer is not under tension, the effect does not occur. Today it is also generally used to describe the heating or cooling of a solid as a reaction to mechanical deformation. Under the usual conditions, this is a result of the thermomechanical description of solid bodies.

root cause

Above the glass transition temperature , the elastic restoring forces between the molecular crosslinking points in elastomers are very small. The hardness results from the entropic restoring forces , which increase with increasing temperature. Therefore, above the glass transition temperature, elastomers become harder with increasing temperature. The stretched elastomer therefore stretches less at a higher temperature.

Dependence of the modulus of elasticity of unfilled elastomers on the temperature

Demonstration experiment

Setup and observation

The effect can be demonstrated in a simple experiment. It is a wheel with rubber spokes, which is also called a Feynman wheel (after Richard Feynman ). The wheel is hung on its axle and the spokes are heated locally, for example by illuminating them with a carbon arc lamp . The wheel then begins to turn and gives the impression of a perpetual motion machine of the second kind, as there is no apparent reason for this movement.

Explanation

The locally heated rubber bands contract due to the heat, which shifts the center of gravity of the wheel a little. As a result, the axis of the wheel is no longer together with the center of gravity, which creates a torque M. The wheel then begins to turn. So here heat is converted into work .

Thermomechanical derivation

For a material with linear thermoplastic material behavior, the stress tensor yields with the Hooke's Law for the Steifigkeitstensor , strain tensor , thermal expansion coefficient matrix and temperature difference to ${\textstyle {\boldsymbol {\sigma }}}$ ${\textstyle \mathbb {\mathbb {C} } }$ ${\textstyle {\boldsymbol {\varepsilon }}}$ ${\textstyle {\boldsymbol {\alpha }}}$ ${\textstyle \Delta \theta }$

${\displaystyle {\boldsymbol {\sigma }}=\mathbb {C} :[{\boldsymbol {\varepsilon }}-{\boldsymbol {\alpha }}\Delta \theta ]{\text{.}}}$

From this it follows for the temperature stresses

${\displaystyle {\frac {\partial {\boldsymbol {\sigma }}}{\partial \theta }}=-\mathbb {C} :{\boldsymbol {\alpha }}=-3K\alpha {\boldsymbol {1}}{\text{,}}}$

where the last term is the isotropic special case with the compression modulus , thermal expansion coefficient (now scalar) and unit matrix . ${\textstyle K}$ ${\textstyle \alpha }$ ${\textstyle {\boldsymbol {1}}}$

The heat conduction equation is (without dependence on internal variables, such as plastic strain)

${\displaystyle \rho c_{V}{\dot {\theta }}=\rho w-\mathrm {div} {\vec {q}}+\theta {\frac {\partial {\boldsymbol {\sigma }}}{\partial \theta }}\cdot {\dot {\boldsymbol {\varepsilon }}}{\text{ .}}}$

From the heat conduction equation, for the adiabatic special case (heat flow ) without a heat source ( ), linearized around the starting temperature , taking into account that ${\displaystyle {\vec {q}}={\boldsymbol {0}}}$ ${\displaystyle w=0}$ ${\displaystyle \theta _{0}}$ ${\displaystyle {\boldsymbol {\varepsilon }}\cdot {\boldsymbol {1}}={\text{sp}}({\boldsymbol {\varepsilon }})={\frac {{\text{d}}V}{{\text{d}}V_{0}}}}$

${\displaystyle {\frac {\dot {\theta }}{\theta _{0}}}=-{\frac {3K\alpha }{\rho c_{V}}}{\dot {\left({\frac {{\text{d}}V}{{\text{d}}V_{0}}}\right)}}{\text{,}}}$

with mass density , mass-specific heat capacity for constant volume , the volume and the time derivative . ${\displaystyle \rho }$ ${\displaystyle c_{V}}$ ${\displaystyle V}$ ${\displaystyle {\dot {(...)}}}$

It can be seen that a positive change in temperature results in a negative change in volume.

Individual evidence

1. ^ Truesdell, Noll: The non-linear theories of mechanics . Springer, 2004, ISBN 3-540-02779-3 , p. 360.
2. ↑ Play of Forces (University of Stuttgart)
3. ↑ Project internship on the Feynman wheel

literature

• John Gough: A description of a property of caoutchouc, or Indian rubber; with some reflections on the cause of the elasticity of this substance . In: Memoirs of the Literary and Philosophical Society of Manchester . Second series. Volume I, 1805, pp. 288–295 (English, digitized versionhttp: //vorlage_digitalisat.test/1%3D~GB%3D2k1XdB3sfLYC~IA%3D~MDZ%3D%0A~SZ%3DPA288~ double-sided%3D~LT%3D~PUR%3D ).
• James Prescott Joule: On some thermo-dynamic properties of solids . In: Philosophical Transactions of the Royal Society of London . tape 149 , 1859, pp. 91–131 , doi : 10.1098 / rstl.1859.0005 (English, digitizedhttp: //vorlage_digitalisat.test/1%3D~GB%3DVVJFAAAAcAAJ~IA%3D~MDZ%3D%0A~SZ%3DPA91~ double-sided%3D~LT%3D~PUR%3D ).
• Clair L. Stong: The amateur scientist. Some delightful engines driven by the heating of rubber bands . In: Scientific American . Volume 224, No. 4 , April 1971, p. 118–122 , doi : 10.1038 / scientificamerican0471-118 (English).
• JG Mullen, George W. Look and John Konkel: Thermodynamics of a simple rubber ‐ band heat engine . In: American Journal of Physics . tape 43 , no. 4 , April 1975, p. 349-353 , doi : 10.1119 / 1.9852 (English).

Web links

• Description of the demonstration experiment with images ( Memento from November 17, 2008 in the Internet Archive )
• Another illustration of the demonstration experiment