Explain Graphs -- adiabatic Expansion of mono- di- and poly- gas

[Shreyans Jain]

"How it can be explained mathematically by dP/dV = -gammaP/V

 

[Chestermiller]

What are your thoughts on this?

 

[Shreyans Jain]

What are your thoughts on this?

I am not able to figure out which has greater slope kind of confused in negative slope of adiabatic

 

[lychette]

I am not able to figure out which has greater slope kind of confused in negative slope of adiabatic

do you understand that ISOTHERMAL means at constant temperature and that ADIABATIC means no heat transfer?

 

[Chestermiller]

Do you know the solution to that differential equation that you wrote down? If so, what is it?

 

[lychette]

The yellow curve shows an isothermal expansion, during the expansion heat energy must be supplied to keep the temperature constant.
The other 3 curves are all adiabatic expansions so no heat energy enters or leaves the gas. Heat energy (internal energy) is removed from the gas and therefore the values of P and V are lower than for the isothermal expansion.
Mathematical analysis will give the details of the curve shapes.
In general adiabatic curves are steeper than isothermal curves...I realize this is not a mathematically rigorous statement but it is helpful ...I hope.
Ps...make sure you are clear about this before you worry about the details of monatomic, diatomic molecules etc !

 

[Shreyans Jain]

Thanks lychette and chestermiller sir, i know about the processes and i also know what happens when heat is taken out but i was not able to get the results by the differential equation.

 

[Shreyans Jain]

The yellow curve shows an isothermal expansion, during the expansion heat energy must be supplied to keep the temperature constant.
The other 3 curves are all adiabatic expansions so no heat energy enters or leaves the gas. Heat energy (internal energy) is removed from the gas and therefore the values of P and V are lower than for the isothermal expansion.
Mathematical analysis will give the details of the curve shapes.
In general adiabatic curves are steeper than isothermal curves...I realize this is not a mathematically rigorous statement but it is helpful ...I hope.
Ps...make sure you are clear about this before you worry about the details of monatomic, diatomic molecules etc !

Sir i know about that but i am not able to get mathemtical result, if possible could you please send me those.
Thanks

 

[Shreyans Jain]

Do you know the solution to that differential equation that you wrote down? If so, what is it?

Sir, i am not able to get the mathematical result

 

[Chestermiller]

Sir, i am not able to get the mathematical result

Are you saying that you have not had a course in differential equations, and do not know how to solve a homogeneous first order linear ordinary differential equation?

 

[Shreyans Jain]

Are you saying that you have not had a course in differential equations, and do not know how to solve a homogeneous first order linear ordinary differential equation?

I know how to solve a homogeneous first order linear ordinary differential equation but there was something missing which i have got it now now thanks.