Q. 7

# Show that the slo

For an isothermal process, the ideal gas equation is given as

PV = constant … (i),

Where

P = pressure

V = volume.

Differentiating on both sides of (i), we get

PdV + VdP = 0

On solving for , we get … (ii)

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),

where

P = pressure,

V = volume,

γ = ratio of specific heat capacities at constant pressure and constant volume.

Differentiating both sides of (ii), we get

V𝛾dP + 𝛾V𝛾-1PdV = 0 which gives … (iv)

Hence, for an adiabatic process, the slope of the p-V diagram is given by -𝛾P/V.

Since 𝛾 > 1, we find that 𝛾P/V is greater than P/V, which concludes that slope of p-V diagram of an adiabatic process is steeper than that of an isothermal process(proved).

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Two vessels A andHC Verma - Concepts of Physics Part 2

4.0 g of helium oHC Verma - Concepts of Physics Part 2

Figure shows two HC Verma - Concepts of Physics Part 2

An amount Q of heHC Verma - Concepts of Physics Part 2

The volume of an HC Verma - Concepts of Physics Part 2

A gas is enclosedHC Verma - Concepts of Physics Part 2

Two samples A andHC Verma - Concepts of Physics Part 2

A sample of an idHC Verma - Concepts of Physics Part 2

An ideal gas (C<sHC Verma - Concepts of Physics Part 2

Half mole of an iHC Verma - Concepts of Physics Part 2