# Question #d1389

##### 1 Answer

For ideal gas on a pV diagram, an adiabatic curve is always steeper than an isotherm if they intersect.

#### Explanation:

The ideal gas equation:

#p# is pressure#V# is volume#n# is number of moles#R# is ideal gas constant#T# is the absolute temperature

For an isothermal process, the right hand side of the ideal gas equation does not change. Which means

#pV = "constant"#

The slope at any point is given by

#{dp}/{dV} = -p/V#

using implicit differentiation or any other methods.

For adiabatic processes, the path would follow a curve of the following form:

#pV^gamma = "constant"#

Differetiating to find the slope

#{dp}/{dV} = -gamma p / V#

This looks very similar to the expression for the slope of isotherm, except that gamma is always > 1 and therefore the slope would be steeper.