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  • The slope of isothermal and adiabatic curves are related as Option: 1 <img alt="Isothermal\ curve\ slope = adiabatic\ curve\ slope" src="/latex-

The slope of isothermal and adiabatic curves are related as 

Option: 1

Isothermal\ curve\ slope = adiabatic\ curve\ slope


Option: 2

Slope \, of \, isothermal\, process= \gamma\, \times Slope \, of \, adiabatic\, process


Option: 3

Slope \, of \, adiabatic\, process = \gamma\, \times Slope \, of \, isothermal\, process


Option: 4

Slope \, of \, adiabatic\, process = \frac{1}{2}\gamma\, \times Slope \, of \, isothermal\, process


Answers (1)

best_answer

As we have learned

Relation between slope of isothermal and adiabatic process -

\frac{dP}{dV}_{isothermal}= -\frac{P}{V}

\frac{dP}{dV}_{adiabatic}= -\gamma \frac{P}{V}

- wherein

Slope \, of \, adiabatic\, process = \gamma\, \times Slope \, of \, isothermal\, process

 

 For isothermal process PV = constant 

\frac{dP}{dV}= \frac{-P}{V} = slope \: \: of \: \: isothermal \: \: curve

For adiabatic process PV^\gamma = constant

\frac{dP}{dV} = - \frac{\gamma P}{V} = slope \: \: of \: \: adiabatic \: \: process \\\\ so \left ( \frac{dP}{dV} \right )_{adiabatic } = \gamma \left ( \frac{dP}{dV} \right )_{isothermal }

 

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Anam Khan

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