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Show that the slope of p –V diagram is greater for an adiabatic process as compared to an isothermal process.
For an isothermal process, the ideal gas equation is given as
PV = constant … (i),
P = pressure
V = volume.
Differentiating on both sides of (i), we get
PdV + VdP = 0
On solving for , we get
For a graph of P versus V, dP/dV indicates the slope.
Hence, for an isothermal process, the slope of the p-V diagram is given by -P/V.
Now for an adiabatic process, the ideal gas equation is
PVγ= constant … (iii),
P = pressure,
V = volume,
γ = ratio of specific heat capacities at constant pressure and constant volume.
Differentiating both sides of (ii), we get