Adiabatic Compression Temperatures

[Natla88]

Hi,

When a gas is compressed, its temperature increases. But what is the formula to calculate this rise? Could you please explain the formula too. This isn't homework btw!

Thanks!

 

[SeniorTotor]

Coefficient of thermal expansion (numerical values are given in handbooks of physics)...
$$\alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P$$
reads also...
$$\Delta T=\frac{\Delta V}{\alpha V}$$

 

[yuiop]

Hi,

When a gas is compressed, its temperature increases. But what is the formula to calculate this rise? Could you please explain the formula too. This isn't homework btw!

Thanks!

For an adiabatic process (no heat energy exchanged with the surroundings) the temperature can be found from

$$T2 = T1 (V1/V2) ^{(y-1)}$$

[EDIT] Note that these formulas are not exact because y is not exactly constant as heat capacity changes with changes in volume and pressure, but it reasonable to assume constant y over small changes in the states.


and the pressure can be found from

$$P2 = P1 (V1/V2) ^y$$

where T1, P1 and V1 are the initial values and T2, P2 and V2 are the final values.

(y) is a constant that depends on the type of gas used and is related to the degrees of freedom that the molecules of gas have. For a diatomic gas the molecules can rotate and part of the energy added to the system is used to increase the rotation rate of the molecules. Temperature is proportional to the linear kinetic energy of the molecules so energy that is used to increase the rotation rate of the molecules does not contribute to the increase in temperature. For a monatomic gas y is about 5/3 while for a diatomic gas y is about 7/5.

Numerical example: If V1 = 100, P1=1 and T1=100 (in degrees kelvin) and V2 = 50 (compression) then T2=158 Kelvin and P2=3.17 for a monatomic gas while T2= 131 kelvin and P2 = 2.63 for a diatomic gas. Note that the increase in temperature and pressure is less for a diatomic gas than a monatomic gas during compression, when the same amount of energy in the form of work has been added to the systems.

For more info see http://en.wikipedia.org/wiki/Adiabatic_process

Hope that helps :)

[EDIT] Note that these equations are aproximations because y is not exactly constant as pressure and volume varies.

 

[zarbanx]

kev has told u all there is nothing much to say except tht y in the equation is Cp/Cv