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This document delves into the fundamental equations governing heat capacities in thermodynamics. It explains the relationship between heat (Q), internal energy change (ΔU), work done (W), and temperature change (ΔT) through equations like C = (ΔU - W) / ΔT. It also discusses the heat capacities at constant volume (CV) and constant pressure (Cp), and their significance in physical processes. The text highlights that while these concepts are broadly applicable, they do not account for latent heats, where temperature remains unchanged.
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HEAT CAPACITIES C = Q/ΔT
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT Then: CV = (ΔU/ΔT)V
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT Then: CV = (ΔU/ΔT)V and for infinitesimal values
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT Then: CV = (ΔU/ΔT)V and for infinitesimal values CV = (∂U/∂T)V
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT Then: CV = (ΔU/ΔT)V and for infinitesimal values CV = (∂U/∂T)V Cp = (∂U/∂T)p
HEAT CAPACITIES C = Q/ΔT But we know that Q = ΔU – W So C = (ΔU – W) / ΔT Then: CV = (ΔU/ΔT)V and for infinitesimal values CV = (∂U/∂T)V Cp = (∂U/∂T)p Cp =(∂U/∂T)V + P (∂V/∂T)P
Heat Capacities • Where (∂V/∂T)P = ∂ (NkT/P) = NkT/P ∂T
Heat Capacities • Where (∂V/∂T)P = ∂ (NkT/P) = NkT/P ∂T This approach will not work for Latent Heats since there is no temperature change.
Heat Capacities • Where (∂V/∂T)P = ∂ (NkT/P) = NkT/P ∂T This approach will not work for Latent Heats since there is no temperature change. Here we define L ≡ Q/m
