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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Topics_in_Thermodynamics_of_Solutions_and_Liquid_Mixtures/01%3A_Modules/1.24%3A_Misc/1.14.25%3A_Equation_of_State-_Perfect_GasAt equilibrium the isothermal dependence of thermodynamic energy on volume is given by equation (b). \[\left(\frac{\partial \mathrm{U}}{\partial \mathrm{V}}\right)_{\mathrm{T}}=\mathrm{T} \,\left(\fra...At equilibrium the isothermal dependence of thermodynamic energy on volume is given by equation (b). (∂U∂V)T=T(∂S∂V)T−p
- https://chem.libretexts.org/Bookshelves/General_Chemistry/General_Chemistry_Supplement_(Eames)/Gases/Real_GasesIn the derivation of the ideal gas law, we assume that there are no attractive forces between the particles and that the particles don't take up any space. Since we know that attractive forces become ...In the derivation of the ideal gas law, we assume that there are no attractive forces between the particles and that the particles don't take up any space. Since we know that attractive forces become important at low temperatures, and that the volume of the particles will be important when the volume is relatively low (meaning pressure is high) we can predict that the ideal gas equation works best at high temperatures and low pressures.
- https://chem.libretexts.org/Bookshelves/General_Chemistry/General_Chemistry_Supplement_(Eames)/Gases/Kinetic-Molecular_TheoryCombining these, the number of collisions increases by s 3 when the volume decreases by 1/s 3 . The pressure is the number of impacts multiplied by the momentum of the particles, mv, where m is the ma...Combining these, the number of collisions increases by s 3 when the volume decreases by 1/s 3 . The pressure is the number of impacts multiplied by the momentum of the particles, mv, where m is the mass of a particle and v is the average velocity. When you calculate the average momentum change from each collision and the average number of collisions per area of wall, the result is P = nmv 2 /3V, where n is the number of particles and V is the volume.
