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.