FrontierScience

Consider a dielectric block with polarization `\(P\) and internal energy \(U\) which obeys` `\[ U(T, P) = CT + f(P)\,,\]`where 𝑓(𝑃) is the polarization-dependent part of the internal energy. where `\(CT\)` is the internal energy of the unpolarized dielectric block, `\(C\)` is the heat capacity of the dielectric block, and `\(T\)` is the absolute temperature. For convenience, any possible volume change of the dielectric block during the polarization process is ignored. Let `\(p\)` represent the total electric dipole moment generated by the polarization of the dielectric, so that \\(p=PV\\) …

\(U=CT\)'

physics

27c865e6-1c87-489b-b7ea-b197fe3356ba

For rising moist air of molar heat capacity `\( c_p \)`, molar latent heat `\( L \)`, molar mass `\( M \)`, the temperature fluctuates with height. You can assume `\[ \frac{\Delta T}{T} = \frac{1 + \alpha \rho_s}{1 + \beta \rho_s \gamma}\frac{\beta}{\alpha}\rho \]` where `\( \alpha = L/(RT), \beta = L/(c_pT), \rho_s = P_s/P, \rho = \Delta P/P, \)` and `\( \gamma = \frac{TdP_s}{P_sdT} \)`. Here, `\( R,T,P,P_s,\Delta \)` are the universal gas constant, air temperature, air pressure, saturated vapour pressure of water (where `\( P_s \)` is a monotonic function of `\(T\)`) and the small fluctu …

`\[ \frac{\Delta T}{\Delta h} = -\frac{Mg\beta}{R\alpha}\frac{1+\alpha \rho_s}{1+\alpha \beta \rho_s} \]`

physics

0ea11f5b-df09-4330-92cc-302a63c22008