How to Solve Thermodynamics Relations for Liquid Alcohol?

In summary, the conversation discusses the study of simple processes of liquid alcohol and its molar volume, molar heat capacity, isobaric coefficient of thermal expansion, and isothermal compressibility coefficient at a constant pressure and temperature. The equations for these values are also provided. The three questions in the conversation involve finding the molar heat capacity at constant volume and temperature, evaluating the work received by alcohol during a process of receiving heat at constant pressure, and finding the rate of change of internal energy at constant pressure with respect to temperature. The solutions to these questions involve using various thermodynamic equations and integrating to find the desired values.
  • #1
fujiwara_sai
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Homework Statement



We propose to study simple processes of liquid alcohol. At T_1, the molar volume of alcohol is V_1 and its molar heat capacity at constant pressure is C_p,m. We assume that its isobaric coefficent of thermal expansion a, and the isothermal compressibilty coefficient B are constant.

a. Find the molar heat capacity (C_v,m) at constant volume and T_1, and the variation of the pressure with temperature at constant volume.

b. starting from an initial state (T_1, V_1), alcohol receives an amt. of heat at constant pressure P, and its final temp. is T_2. Evaluate the work received by alcohol during the process.

c. Find a formal expression for the rate of change with temperature of the internal energy of the liquid at constant pressure.


Homework Equations



isothermal coefficient of thermal expansion, a = 1/V * (dV/dT)_p
isothermal compressibilty coefficient B, -1/V * (dV/dP)_T

C_p = C_v + TVa^2/B ------ eqn (1)

The Attempt at a Solution



For qns a, i have no idea how to go about finding C_v,m. So i simply used the direct relatonship in eqn (1) to find C_v,m which i highly doubt its correct.
for the second part of the qns,
I used P=P(T,V)
-> dP = MdT + NdV
doing some algebric manipulation: dV = (1/N * dP) - (M/N * dT)
by comparing coefficients from the derived eqn of V=V(T,P)...
i got my final dP = (a/B * dT) - (1/VB *dV)
at constant volume: (dP/dt)_V = a/B

is this correct?

For qns b, here's what i attempted:

(T_1, V_1) ----> (T_2, V_2) at constant P.
Using U=U(T,P) thermodynamics relationship and letting dP=0
i get dU = (C_p - PVa)*dT
by integrating from T_1 to T_2, i will get the change in U.
then to find the Q received, i used H=H(T,P)
where in the end i get dH=Q=C_p * dT
again i integrate to find Q.
then finally i use first law U= Q+W to find W.
is this correct?

For qns c,

i used U=U(T,P)
at constant P, i get dU=(C_P-PVa)*dT

im not sure if this is correct or not...

thanks a lot for helping me out
 
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  • #2
is there any kind soul who can help me?

Thanks!
 

FAQ: How to Solve Thermodynamics Relations for Liquid Alcohol?

1. What is the definition of thermodynamics?

Thermodynamics is the branch of physics that studies the relationship between heat, energy, and work. It deals with the transfer of energy and its effects on physical systems.

2. What are the four laws of thermodynamics?

The four laws of thermodynamics are:

  1. The first law, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another.
  2. The second law, also known as the law of entropy, states that the total entropy of a closed system will always increase over time.
  3. The third law states that it is impossible to reach absolute zero (0 Kelvin) through a finite number of steps.
  4. The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

3. What is the difference between a closed and an open system in thermodynamics?

A closed system is a system in which no matter can enter or leave, but energy can be exchanged with the surroundings. An open system is a system in which both matter and energy can be exchanged with the surroundings.

4. What are thermodynamic relations?

Thermodynamic relations are mathematical equations that describe the relationships between different thermodynamic variables, such as temperature, pressure, volume, and energy. These relations are derived from the four laws of thermodynamics and are used to analyze and understand thermodynamic systems.

5. How are thermodynamic relations used in practical applications?

Thermodynamic relations are used in a variety of practical applications, such as designing and optimizing energy systems, predicting and analyzing the behavior of materials under different conditions, and understanding the efficiency of industrial processes. They are also used in fields such as chemistry, engineering, and environmental science to solve problems and make predictions based on thermodynamic principles.

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