We have four objects in our possession the masses heat capac

We have four objects in our possession; the masses, heat capacities, and initial temperatures are as follows: What we would like to do is to devise some process(cs) that allow heat ann/or work interactions between these for objects With no net change in the environment, what is the minimum temperature that you could attain in any one of the four objects? In which object would you attain this temperature? Repeat if you desired the maximum possible temperature.

Solution

Because heat can only flow from hot to cold, the only way, by spontaneous heat transfer alone, to get a cold temperature, is to begin with a cold temperature.

Hence, you simply identify the coldest material and its initial temperature, and call that your working answer. We\'ll discuss below, why you can\'t have any other answer.

There can be a possibility to get an even colder temperature, but what you need is a very interesting situation, that I can\'t imagine working for any of these objects. You\'d need a method for an object to undergo either a physical change or a chemical change that has a spontaneous increase in its entropy to simultaneously allow for a self-cooling chill.

One example of this, is the sudden expansion of a liquid in to a vacuum. That is part of the process of how refrigeration works, where it throttles liquid (a frictional drop in pressure) to a two-phase liquid-vapor at low pressure, and the loss of pressure is what enables it to be liquid+vapor at a lower temperature.

In this set of objects, there are no such examples. I can\'t see any chemical reaction we can make that would generate entropy and absorb chemical energy. And I can\'t see the phase drop thing.

As for work being involved, well here is the thing. Heat doesn\'t just spontaneously convert in to work, so that an object can cool off. Just imagine how weird it would be for you to take your bike from right beside your furnace, to outside on a cold day, and have it move without pedaling.

Work can convert to heat, as is exactly the process that happens when friction brings motion to a halt. But our goal wasn\'t to achieve a high temperature. It was to achieve a low temperature.

so Bar of Chromium attains the minimum temperature.