How to Solve for the Fractional Change in Temperature in an Adiabatic Process?

In summary, the conversation discusses the relationship between the fractional changes in temperature and pressure for an ideal gas. The equations PV^{\gamma}=\rm constant and nC_vdT=-PdV are mentioned, and it is shown that \frac{dP}{P}=\frac{dT}{T} for an ideal gas. The person asking for help eventually solves the problem.
  • #1
Gyroscope

Homework Statement


3.14
(0.5) How is the fractional change in temperature related to [tex]\frac{dT}{T}[/tex] the fractional change in pressure [tex]\frac{dP}{P}[/tex] ?
(IPhO 2006)

Homework Equations



[tex]PV^{\gamma}=\rm constant[/tex]

The Attempt at a Solution



nC_vdT=-PdV (1), dV/dP=-nRT/(P^2)

If I substitute dV in the equation (1) it does not give the right result.

Can someone help me, please? :tongue2:

Thanks my dear friends.
 
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  • #2
It appears you are talking about an ideal gas? Then in
[tex]P=nRT/V[/tex]
we see right away that P changes the same way as T. This is shown mathematically as

[tex]\frac{dP}{dT}=\frac{nR}{V},[/tex]

[tex]\frac{dP}{P}=\frac{nRdT}{PV}=\frac{dT}{T}.[/tex]
 
  • #3
Thanks marcusl for your help. But you are wrong. :( I already solved it. Thanks anyway my dear friend.
 
  • #4
Sorry! Glad you solved it.
 

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no heat exchange between the system and its surroundings. This means that the system is completely isolated and there is no transfer of energy in the form of heat.

What is the difference between adiabatic and isothermal processes?

The main difference between adiabatic and isothermal processes is that in an adiabatic process, there is no heat exchange between the system and its surroundings, while in an isothermal process, the temperature of the system remains constant. In other words, an adiabatic process does not involve any change in the internal energy of the system, while an isothermal process does not involve any change in the temperature of the system.

What are some practical applications of adiabatic processes?

Adiabatic processes are commonly used in the field of thermodynamics, particularly in the study of engines and heat pumps. They are also important in the study of atmospheric processes, such as the formation of clouds and the behavior of air masses.

What is the first law of thermodynamics and how does it relate to adiabatic processes?

The first law of thermodynamics states that the total energy in a closed system remains constant. In an adiabatic process, there is no heat exchange between the system and its surroundings, so the change in internal energy of the system is equal to the work done on or by the system. This is in line with the first law of thermodynamics.

What are some examples of adiabatic processes?

Some common examples of adiabatic processes include the compression or expansion of a gas in a piston, the expansion of a gas in a turbine, and the movement of air masses in the atmosphere. In these processes, there is no heat exchange with the surroundings, making them adiabatic.

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