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

1. Mar 8, 2017

### Shreyans Jain

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

2. Mar 8, 2017

### Staff: Mentor

What are your thoughts on this?

3. Mar 8, 2017

### Shreyans Jain

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

4. Mar 8, 2017

### lychette

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

5. Mar 8, 2017

### Staff: Mentor

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

6. Mar 8, 2017

### 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 realise this is not a mathematically rigorous statement but it is helpful ....I hope.

7. Mar 8, 2017

### 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.

8. Mar 8, 2017

### Shreyans Jain

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

9. Mar 8, 2017

### Shreyans Jain

Sir, i am not able to get the mathematical result

10. Mar 8, 2017

### Staff: Mentor

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?

11. Mar 9, 2017

### Shreyans Jain

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.