# DeltaG and DeltaA calculation for heating a gas at constant volume

• zacc
In summary, the conversation revolves around solving a problem involving an ideal gas undergoing multiple changes of state. One specific step asks for the calculation of the change in Gibbs Energy (ΔG) and Helmholtz energy (ΔA) for heating 0.1 mol of the gas from 20 oC to 120 oC at constant volume. The individual terms for each calculation are discussed, with the second term being the main issue due to the constant temperature not being applicable in this problem. The gas is not specified as mono-atomic or diatomic. The equations ΔG=ΔH-Δ(TS) and ΔA=ΔU-Δ(TS) are suggested for use in the calculations
zacc
Summary:: Gibbs and Helmholtz energies calculations for heating an ideal gas at constant volume

I am solving a problem involving an ideal gas that undergoes several chained changes of state. One of the steps asks to calculate the change in Gibbs Energy (DeltaG) and Helmholtz energy (Delta A) for 0.1 mol of the gas being heated from 20 oC to 120 oC at constant volume. The initial volume is 4.0 L. I am stuck here.

In natural variables dG is given by dG=VdP-SdT. The first term is easily calculated by replacing V by nRT/P and integrating.The second term is what I don't know what to do with it. Every textbook that I have checked so far have examples where T is constant so the second term is not an issue but not in this problem. The same problem is also found with Helmholtz energy: dA=-PdV - SdT. The first term is zero because dV=0 but then I am stuck again with the second term.

Any help is greatly appreciated!

Is this a homework problem?

Hello. Not really. It is a problem that I am solving on my own from an old textbook in Thermodynamics.

zacc said:
Hello. Not really. It is a problem that I am solving on my own from an old textbook in Thermodynamics.
Well, anyway, homework-like problems are considered homework problems, so I am moving it to a homework forum.

Can you please provide an exact word-for-word statement of the problem?

Is the gas mono-atomic, diatomic, or something else?

You should be using ##\Delta G=\Delta H-\Delta (TS)## and ##\Delta A=\Delta U-\Delta (TS)##

Last edited:

## 1. What is the formula for calculating DeltaG and DeltaA for heating a gas at constant volume?

The formula for calculating DeltaG (change in Gibbs free energy) is ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. The formula for calculating DeltaA (change in Helmholtz free energy) is ΔA = ΔU - TΔS, where ΔU is the change in internal energy.

## 2. How do you determine the values of ΔH, ΔS, and ΔU for a gas at constant volume?

The values of ΔH, ΔS, and ΔU can be determined experimentally by measuring the change in temperature and pressure of the gas. The change in temperature can be used to calculate ΔU using the formula ΔU = nCvΔT, where n is the number of moles of gas and Cv is the molar heat capacity at constant volume. The change in pressure can be used to calculate ΔH using the formula ΔH = nCpΔT, where Cp is the molar heat capacity at constant pressure. The change in entropy, ΔS, can be calculated using the formula ΔS = nCp ln(T2/T1), where T1 and T2 are the initial and final temperatures, respectively.

## 3. How does the value of temperature affect the calculations for DeltaG and DeltaA?

The value of temperature is directly related to the calculations for DeltaG and DeltaA. As temperature increases, the value of ΔS increases, leading to a decrease in both DeltaG and DeltaA. This is because at higher temperatures, the gas molecules have more energy and are more disordered, resulting in a higher entropy. Additionally, at constant volume, the change in enthalpy (ΔH) and internal energy (ΔU) will also increase with an increase in temperature, leading to a decrease in DeltaG and DeltaA.

## 4. Can the calculations for DeltaG and DeltaA be used for gases at varying volumes?

No, the calculations for DeltaG and DeltaA are specifically for gases at constant volume. If the volume of the gas changes, the equations for calculating DeltaG and DeltaA will be different. For gases at varying volumes, the ideal gas law (PV = nRT) can be used to calculate the change in enthalpy (ΔH) and internal energy (ΔU), which can then be used in the equations for DeltaG and DeltaA.

## 5. What is the significance of calculating DeltaG and DeltaA for heating a gas at constant volume?

Calculating DeltaG and DeltaA for heating a gas at constant volume allows us to understand the thermodynamics of the process. It tells us how much energy is required to heat the gas and how much of that energy is available to do work. This is important in many industries, such as in the design of engines and power plants, where understanding the thermodynamics of gas heating is crucial for efficient operation.

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