The McDLT and the arrow of time

The inexorable arrow of time
Years ago McDonald’s introduced a lettuce and tomato hamburger called the McDLT, where the (hot) hamburger was kept on one side of the container and the (cold) lettuce and tomato on the other.  The patented container was intended to keep the hot side hot and the cool side cool.  When you received your order, you would combine the two sides.   The burger was similar to, and presumably a competitor to Burger King’s whopper, distinguished by the unique packaging.  The product sought exclusion or at least a reprieve from the second law of thermodynamics – but physical laws, unlike those for speeders and tax evaders, brook no exceptions, as we shall see.

The second law is fairly simple: entropy always increases, and the change in entropy is the heat transferred, divided by the temperature at which it is transferred.  The temperature is measured in absolute units, such as Kelvin rather than Celsius, so that the lowest possible temperature is zero degrees Kelvin.  This is the version of the law for isolated systems.

For the McDLT, as the cool side heats up and the hot side cools down, the “cold side” has a change in entropy of (H)/Tcold , where H is the heat transferred from the hot side to the cold side which is at a temperature Tcold , and the “hot side” has a change of (-H)/Thot , where the negative sign is because the hot side loses that heat.  Hence the total change of entropy is H(1/Tcold – 1/Thot ).

Note that, as long as the heat H is positive, the entropy increases. All the other laws of physics are perfectly fine with the hot side getting hotter, and the cold side getting colder, only the second law explains this situation.  Further, note that if we were to look backwards in time, the hot side does get hotter and the cold side colder.  The second law of thermodynamics is the physical law which gives the origin of the arrow of time, and indeed the origin of causality.

All of this was lined up on one side, against, on the other side, the weight and resourcefulness of the McDonald’s corporation.  The McDLT had a proud run of about 6 years from 1984 to 1990, but in the end succumbed.  In part, due to being pierced by the inexorable arrow of time.

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