Chestermiller said:I don't think this is what they want you to do. I think what they want is to start out with dH = TdS+VdP, and then use the the chain rule to express dS(V,T) and dP(V,T). The partial of S with respect to T is known in terms of Cv. The partial of S with respect to V is obtained from a Maxwell relationship.
Yes. Seeing that solution, the steps that I recommended to follow are perfect.grandpa2390 said:I'm glad you're here. I'm not sure what I am supposed to do exactly. I'm trying to figure it out.
the problem is to show that enthalpy as a function of volume and temperature can be expressed in the form
##dH = (P + π_T - \frac{1}{k_T})dV + (C_v + V(\frac{∂P}{∂T})_v)dT##
by following the steps below.
the first step is to express dH(V,T) as a state function.
I thought the state functions were something to memorize.
I'm going to write out what you said, and think about it. Because that is the first step. thanks ;)
if you want the rest of the steps, I'll post them. I just don't want to seem like I am asking for the solution.
Forgive me it's been so long I'm going to retake multivariable in the summer. But I don't know how to use the chain rule here.Chestermiller said:I don't think this is what they want you to do. I think what they want is to start out with dH = TdS+VdP, and then use the the chain rule to express dS(V,T) and dP(V,T). The partial of S with respect to T is known in terms of Cv. The partial of S with respect to V is obtained from a Maxwell relationship.
Chestermiller said:Yes. Seeing that solution, the steps that I recommended to follow are perfect.
Chet
Chestermiller said:I don't think this is what they want you to do. I think what they want is to start out with dH = TdS+VdP, and then use the the chain rule to express dS(V,T) and dP(V,T). The partial of S with respect to T is known in terms of Cv. The partial of S with respect to V is obtained from a Maxwell relationship.
No. But you can also start with your equation for dU interns of dT and dV, and add PdV+VdP to get dH.grandpa2390 said:are you saying to use the chain rule on dH to get the dS and dP?
Chestermiller said:No. But you can also start with your equation for dU interns of dT and dV, and add PdV+VdP to get dH.
but I'm not getting why this goes in parenthesis before the dV.Chestermiller said:No. But you can also start with your equation for dU interns of dT and dV, and add PdV+VdP to get dH.
Chestermiller said:No. But you can also start with your equation for dU interns of dT and dV, and add PdV+VdP to get dH.
A state function is a thermodynamic property that depends only on the current state of a system, and not on how the system arrived at that state. In other words, it is independent of the path or process by which the system reached its current state.
dH(V,T) is expressed as a state function by considering the change in enthalpy (H) as a function of volume (V) and temperature (T). This means that the value of dH will be the same for the same change in volume and temperature, regardless of the path taken to reach that change.
Expressing dH(V,T) as a state function allows us to simplify thermodynamic calculations and make predictions about a system's behavior. It also helps us understand the relationships between different thermodynamic properties, and how they are affected by changes in volume and temperature.
When dH(V,T) is expressed as a state function, its units are typically joules per mole (J/mol). This unit reflects the change in enthalpy per mole of substance in the system.
No, dH(V,T) cannot be measured directly as a state function. Instead, it is calculated using other thermodynamic properties such as internal energy, pressure, and volume. However, once dH(V,T) is expressed as a state function, its value can be used in calculations to predict changes in enthalpy of a system.