You see this stated as an equation to the right. The net work done by the engine during
a cycle equals the heat transferred into the engine from the hot reservoir minus the heat
that flows out to the cold reservoir. Heat that flows into the engine from the hot reservoir
is called Qh, and heat that flows out to the cold reservoir is called Qc. We treat both Qh
and Qc as positive quantities. This means the net flow of heat equals QhíQc. If heat
flows only out of the engine during a process in an engine cycle, then the net heat flow
for that process is negative.
This equation is a special case of the first law of thermodynamics. The law states that
the net heat flow equals the work done plus any change in internal energy. Since the
internal energy is not changed after a complete engine cycle (the engine returns to its
initial state), the net work done by the engine equals the net flow of heat.During an engine cycle, the heat
transfers are as shown. What is
the net work done by the
engine?
W = QhíQc
W= 3200 J í 1800 J
W= 1400 J
20.4 - The ideal gas law and heat engines
Many engines use a gas as their working substance. Heat is transferred to the working
substance, which expands and does work. Water (both in liquid and gaseous form) is
another common working substance. However, water vapor is far from an ideal gas,
and in this textbook, we focus on an ideal gas as the working substance.
In addition to the first law of thermodynamics, the ideal gas law is very useful in
analyzing the processes in an engine cycle. Here, we want to briefly review this law,
and show how it is used in analyzing heat engines. The ideal gas law relates pressure,
volume, temperature and the amount of gas. You see the law stated in Equation 1.
In the heat engines we consider, the quantity of gas enclosed by the container is
constant. This leaves three variable properties of a gas in the ideal gas law: the gas’s
pressure, volume and temperature. The product of the pressure and volume is
proportional to the temperature. If the temperature of the gas increases, for instance,
then the product of its pressure and volume must increase, as well.
The first law of thermodynamics states that when heat flows into an engine, the heat
energy increases the gas’s internal energy and/or causes it to do work. A change in
internal energy will be reflected in the gas’s temperature; greater internal energy means
a higher temperature. This means the volume or the pressure of the gas will increase,
or both.To apply these two principles, consider Example 1. The piston is locked in place so that
the gas can do no work. This means that the heat transferred to the engine solely
increases the internal energy of the gas. That increase in internal energy is reflected by
an increase in temperature. Since the piston is locked, the volume of the gas is constant
and the ideal gas law enables us to conclude that its pressure must increase
proportionally to the temperature increase.Ideal gas law
PV = nRT
Whenn is constant:
P = pressure, V = volume
n = number of moles of gas
R = gas constant
T = temperature (K)
(^376) Copyright 2007 Kinetic Books Co. Chapter 20