Van der waals equation and molar specific heat

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SUMMARY

The Van der Waals equation of state, represented as (p + an²/v²)(v - nb) = nRT, describes the behavior of real gases. The discussion focuses on demonstrating that the partial derivative of molar specific heat at constant volume (C_v) with respect to volume (V) at constant temperature is zero, expressed mathematically as (∂C_v/∂V)_T = 0. This involves understanding the definition of heat capacity and calculating internal energy (U) using the Van der Waals equation.

PREREQUISITES
  • Understanding of the Van der Waals equation of state
  • Knowledge of thermodynamic concepts, specifically heat capacity
  • Familiarity with internal energy calculations
  • Basic proficiency in calculus for partial derivatives
NEXT STEPS
  • Study the derivation of the Van der Waals equation of state
  • Learn about the relationship between internal energy and heat capacity
  • Explore the implications of (∂C_v/∂V)_T = 0 in thermodynamics
  • Investigate real gas behavior compared to ideal gas laws
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying physical chemistry, chemical engineering, and anyone interested in the properties of real gases.

koustav
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the van der waals equation of state is given by (p+an^2/v^2)(v-nb)=nRT.how to show that for a gas obeying the above equation of state (∂Cv/∂V) (taking temperature constant)=0?
 
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Just write out what the heat capacity means.
##C_v = \left(\frac{\partial{Q}}{\partial{T}}\right)_v = \left(\frac{\partial{U}}{\partial{T}}\right)_v##
You know how to calculate the internal energy U? Write it using the equation of state.
 
please explain vividly
 

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