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03 Thermal Physics (Ideal Gas (Pressure-Volume Law (Effect of \(\Delta V\)…

- - - - For an ideal gas:
        \(U=E_K\)
        
        \(U=\frac{3}{2}Nk_bT\)
        
        \(U=\frac{3}{2}nRT\)
        
        \(U=\frac{3}{2}pV\)
  - - - Average velocity of gas particles remain unchanged
        
        Molecules collide with container walls less frequently
        
        Rate of change of momentum at walls decreases
        
        Force decreases; pressure decreases
- - - - Of one particle
        
        \(\overline{E}_k=\frac{3}{2}k_bT\)
      - Average Speed
        
        \(\frac{1}{2}mv^2=\frac{3}{2}k_bT\)
        
        \(v=\sqrt{\frac{3k_bT}{m}}\)
      - Of the gas
        
        \(\overline{E}_k=\frac{3}{2}Nk_bT\)
    - - Can be converted to number of particles using Avogrado's constant
        
        \(N=n\cdot N_A\)
    - - \(R=N_A\cdot k_b\)
        
        \(pV=n(N_Ak_b)T\)
        
        \(pV=Nk_bT\)
      - Energy per unit temperature per mole
        \(JK^{-1}\textrm{mol}^{-1}\)