In Fig., Curves AB and CD represent The Relation Between Pressure P and Volume V of An Ideal Gas. One Of The Curves Represents An Isothermal Expansion And The Other Represents An Adiabatic Expansion. Which Curve Represents An Adiabatic Expansion?                                                                             

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Question

In Fig., curves AB and CD represent the relation between pressure P and volume V of an ideal gas. One of the curves represents an isothermal expansion and the other represents an adiabatic expansion. Which curve represents an adiabatic expansion?

                                                                            

Solution

Correct option is

Curve CD

 

For isothermal expansion PV =  constant. Partially differentiating we have

              

Or                           

 

Partially differentiating we have

 

  Or                       

Thus the slope at any point on the adiabatic curve is  times that for isothermal curve. Hence curve CD represents adiabatic expansion.

Testing

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