mirror of
https://github.com/CoolProp/CoolProp.git
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131 lines
4.2 KiB
Plaintext
131 lines
4.2 KiB
Plaintext
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.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
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.. |dT| replace:: :math:`\partial T`
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.. |dv| replace:: :math:`\partial V`
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.. |ds| replace:: :math:`\partial S`
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.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
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.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
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.. |dvdT_p| replace:: :math:`\left(\frac{\partial V}{\partial T}\right)_P`
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================== ============= ====================================================================================
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p
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------------------ ------------- ------------------------------------------------------------------------------------
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|dT| 1
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|dV| |dVdT_p|
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|ds| :math:`c_p/T`
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================== ============= ====================================================================================
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Building a table with the held-constant variable on the right side and
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.. math::
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(\partial T)_P=-(\partial P)_T=1
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.. math::
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(\partial V)_P=-(\partial P)_V=\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial S)_P=-(\partial P)_S=\frac{C_p}{T}
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.. math::
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(\partial U)_P=-(\partial P)_U=C_P-P\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial H)_P=-(\partial P)_H=C_P
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.. math::
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(\partial G)_P=-(\partial P)_G=-S
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.. math::
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(\partial A)_P=-(\partial P)_A=-S-P\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial V)_T=-(\partial T)_V=-\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial S)_T=-(\partial T)_S=\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial U)_T=-(\partial T)_U=T\left(\frac{\partial V}{\partial T}\right)_P+P\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial H)_T=-(\partial T)_H=-V+T\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial G)_T=-(\partial T)_G=-V
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.. math::
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(\partial A)_T=-(\partial T)_A=P\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial S)_V=-(\partial V)_S=\frac{C_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+\left(\frac{\partial V}{\partial T}\right)_P^2
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.. math::
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(\partial U)_V=-(\partial V)_U=C_P\left(\frac{\partial V}{\partial P}\right)_T+T\left(\frac{\partial V}{\partial T}\right)_P^2
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.. math::
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(\partial H)_V=-(\partial V)_H=C_P\left(\frac{\partial V}{\partial P}\right)_T+T\left(\frac{\partial V}{\partial T}\right)_P^2-V\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial G)_V=-(\partial V)_G=-V\left(\frac{\partial V}{\partial T}\right)_P-S\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial A)_V=-(\partial V)_A=-S\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial U)_S=-(\partial S)_U=\frac{PC_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+P\left(\frac{\partial V}{\partial T}\right)_P^2
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.. math::
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(\partial H)_S=-(\partial S)_H=-\frac{VC_P}{T}
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.. math::
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(\partial G)_S=-(\partial S)_G=-\frac{VC_P}{T}+S\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial A)_S=-(\partial S)_A=\frac{PC_P}{T}\left(\frac{\partial V}{\partial P}\right)_T+P\left(\frac{\partial V}{\partial T}\right)_P^2+S\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial H)_U=-(\partial U)_H=-VC_P+PV\left(\frac{\partial V}{\partial T}\right)_P-PC_P\left(\frac{\partial V}{\partial P}\right)_T-PT\left(\frac{\partial V}{\partial T}\right)_P^2
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.. math::
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(\partial G)_U=-(\partial U)_G=-VC_P+PV\left(\frac{\partial V}{\partial T}\right)_P+ST\left(\frac{\partial V}{\partial T}\right)_P+SP\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial A)_U=-(\partial U)_A=P(C_P+S)\left(\frac{\partial V}{\partial P}\right)_T+PT\left(\frac{\partial V}{\partial T}\right)_P^2+ST\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial G)_H=-(\partial H)_G=-V(C_P+S)+TS\left(\frac{\partial V}{\partial T}\right)_P
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.. math::
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(\partial A)_H=-(\partial H)_A=-\left[S+P\left(\frac{\partial V}{\partial T}\right)_P\right]\left[V-T\left(\frac{\partial V}{\partial T}\right)_P\right]+PC_P\left(\frac{\partial V}{\partial P}\right)_T
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.. math::
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(\partial A)_G=-(\partial G)_A=-S\left[V+P\left(\frac{\partial V}{\partial P}\right)_T\right]-PV\left(\frac{\partial V}{\partial T}\right)_P |