amount of work done by the paddles, was always proportional to the increase in the
temperature of the water. This proved a relationship between mechanical energy and
temperature.
Joule used British units. In his experiments, he calculated that 772.5 foot-pounds of
work would increase the temperature of one pound of water by one degree Fahrenheit.
Today, that value has been refined to 778 foot-pounds. Joule’s measurement was
impressively accurate.
Joule also knew how to use the specific heat of water to relate an amount of heat
transferred to a quantity of water to its increase in temperature. He knew how much
heat it would take to raise the temperature of a given amount of water by one degree,
and with his apparatus, he could also calculate how much mechanical energy it would
take to do the same. He showed that one calorie of heat equals an amount of
mechanical energy that today we would describe as 4.19 J. (Since scientists today
know heat is just one form of energy, they do not use the calorie unit as often, but
instead use the joule as the unit for all forms of energy, as well as for work.)
Modern scientists still differentiate between heat (the transfer of energy) and the internal
energy of an object. Heat changes the internal energy of an object or system, just as
work does. Work and heat are two ways to change some form or forms of an object’s
energy. They reflect a process. It does not make sense to refer to “the work of an object” or “the heat of an object.” Rather, it is correct to state
how much work is done on or by an object, or how much heat is transferred into or out of the object. The result is a change in the object’s
energy.
Heat as energy
Joule showed heat is a form of energy
Change of PE proportional to:
·water temperature increase
·heat required for same increase20.3 - Heat engines
A heat engine uses the energy of heat to do work. Many engines have been designed
to take advantage of heat energy. To cite two: A steam engine in an old locomotive and
the internal combustion engine in a modern automobile both use heat as the source of
energy for the work they do.
A heat engine is shown on the right. It is the container with a lid and piston on top,
between a hot reservoir on the left and a cold reservoir on the right. In the engines we
will consider, the container encloses a gas. The gas is cooler than the hot reservoir but
warmer than the cold reservoir. Heat flows spontaneously from the hot reservoir into the
gas in the engine, where the energy can be used to do work. Heat will also flow
spontaneously from the gas to the cold reservoir. Otherwise, the container is insulated
and no heat flows through any other mechanism into or out of the engine.
The reservoirs are large enough that they can supply or absorb as much heat as we
like. We control the flow of heat between a reservoir and the container by opening a
hole in the insulating wall to allow heat to flow, and closing it to stop the flow. The
reservoirs are not part of the system we consider when applying the first law of
thermodynamics.
The amount of gas in the engine stays constant. The temperature and pressure are
assumed to be the same everywhere in the gas at any moment. When we analyze a
heat engine, we will assume it is ideal: that there is no friction to reduce its efficiency
and that heat flows uniformly and instantly through the system.
The engine goes through a sequence of processes that collectively are called an engine
cycle. (One process or step in an engine cycle is sometimes called a stroke.) At the end
of each cycle, the engine returns to its initial state. For instance, during one process,
heat might flow into the engine from the hot reservoir so the piston rises. During another
process, heat might flow out to the cold reservoir as the piston falls. No matter what the
processes, at the end of an engine cycle, the engine returns to its initial configuration:
The piston is in its initial position and the gas is back to its initial volume, pressure and
temperature.
Since the gas returns to its initial state, its internal energy does not change during a
complete engine cycle. This means we can concentrate on the two other quantities in
the first law, namely heat and work. To apply the first law and other equations, we
consider the work done by the gas. The gas does positive work as it lifts the piston. If
the piston moves down and compresses the gas during another part of the cycle, the
gas does negative work.
The distance the piston moves up or down might be the same. However, the amount of
work that occurs will typically differ, since the purpose of the engine is to do net positive
work on the piston during a complete engine cycle. The gas applies more force when it
expands (to move a crankshaft, for example) than when it contracts, so the net work
done by the engine in a cycle is positive. The net transfer of heat into the engine during
a complete engine cycle equals the net work it does. The net transfer of heat equals the
heat in from the hot reservoir minus the heat out to the cold reservoir.
Heat engines
Heat flows into engine
Engine uses heat to do work
Heat flows out of engine
Engine cycle: system returns to initial
state