What is the Efficiency of a Gas Machine in an A->B->C Change?

In summary, the conversation discusses the task of obtaining Q, the heat energy received through an A-B-C change, and the usefulness of a machine. The equations W=pV and PV=nRT are mentioned, and the solution process is explored through the use of these equations and the ideal gas law. The concept of heat transfer is also mentioned as a way to obtain Q.
  • #1
the_man
14
0

Homework Statement



The task is to get Q, that gas has received through A-B-C change?
Second task is to get usefulness of the machine?

http://img40.imageshack.us/img40/8372/toplinaabc.jpg [Broken]

Homework Equations



W=pV

The Attempt at a Solution



If I use W=pV i get 0 from A->B so i can't get usefulness. No idea.
 
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  • #2
To get the heat energy in or out of system one requires the value of the number of moles of gas and the gas constant R or the temperatures at some points on the graph.
 
  • #3
So from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR?

from B->C formula is W=p2(v2*v1) and with ideal gas dT=(p2(v2-v1))/nR?

But how to get Q from that?
 
  • #4
the_man said:
So from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR?

from B->C formula is W=p2(v2*v1) and with ideal gas dT=(p2(v2-v1))/nR?

But how to get Q from that?

from A->B formula is PV=nRT then I get dT=((p2-p1)*v1)/nR ...yes

from B->C formula is W=p2(v2*v1) ...replace * by -

dT=(p2(v2-v1))/nR ...yes

To get the heat transfer one can use [itex]\Delta[/itex]U = [itex]\Delta[/itex]Q + [itex]\Delta[/itex]W where U is the internal energy.
 
  • #5
okay man, thanks!
 

What is gas temperature and how is it measured?

Gas temperature refers to the average kinetic energy of the molecules in a gas. It can be measured using a thermometer, which measures the expansion or contraction of a gas in response to changes in temperature.

Why does gas temperature change from point A to B to C?

Gas temperature changes due to a variety of factors, such as changes in pressure, volume, and energy input. In a closed system, the ideal gas law (PV=nRT) explains how changes in pressure and volume can affect the temperature of a gas. Additionally, energy input in the form of heat or work can also cause changes in gas temperature.

What are some common methods for controlling gas temperature?

Some common methods for controlling gas temperature include adjusting the pressure or volume of the gas, using a heat source or heat sink to add or remove energy, and using a thermostat to maintain a specific temperature.

How does gas temperature affect the behavior of gases?

Gas temperature plays a crucial role in determining the behavior of gases. At higher temperatures, gas molecules have more kinetic energy and move faster, resulting in increased pressure and volume. At lower temperatures, gas molecules have less kinetic energy and move slower, resulting in decreased pressure and volume.

What is the relationship between gas temperature and the speed of sound?

The speed of sound in a gas is directly proportional to the square root of the gas temperature. This means that as gas temperature increases, so does the speed of sound. This relationship is described by the equation c=√(γRT), where c is the speed of sound, γ is the adiabatic index, R is the gas constant, and T is the temperature in Kelvin.

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