Thermodynamics Signs question

[Payne0511]

Homework Statement

A gas piston is filled with propane and oxygen at room temperature to a pressure of 1
atm. The surroundings are 1 atm and room temperature. When triggered with a sparking
device, the propane reacts with the oxygen to produce lots of heat. Assume the system is
infinitely flexible (constant pressure is maintained at all times) and that the surroundings
are infinitely large (the properties of the surroundings never change).
C₃H₈(g) + O₂(g) >> CO₂(g) + H₂O(g) + q

Balanced I believe it becomes... C₃H₈(g) + 5O₂(g) >> 3CO₂(g) + 4H₂O(g) + q

I have to fill in a table for two Times. 1. Immediately following reaction, and 2. Long after, in thermodynamic equil. For the variables, dV, dT, dn_total, w, q, and dU.

We are to assume the rxn takes some measurable amt of time, but does not equil with surroundings until the rxn is complete.

Homework Equations

w=-P_extdV
dU=q+w
dT=dV/(nc)

The Attempt at a Solution

Since its Isobaric, assuming it will expand, is a closed system, and is exothermic. For Immediately after rxn:
dV= +
dT= +
dn= +
w= -
q= -
dU= -

For long after the rxn:
dV= 0
dT= 0
dn= 0
w= 0
q= 0
dU= 0

thanks for anyone's help, it will be greatly appreciated.

 

[nate808]

Thank you for your post. It seems that you have a good understanding of the situation and the equations involved. However, there are a few things that need to be clarified in order to fill in the table accurately.

Firstly, for the immediately after reaction table, the change in volume (dV) will depend on the amount of reactants and products present. Since you have not specified the initial amounts of propane and oxygen, it is difficult to determine the exact change in volume. However, we can assume that the volume will increase as the number of moles of gases increases due to the production of CO2 and H2O. Therefore, dV would be a positive value.

Similarly, the change in temperature (dT) will also depend on the amount of heat (q) released during the reaction. Since the reaction is exothermic, the temperature of the system will increase. Therefore, dT would also be a positive value.

The change in the total number of moles (dn) will depend on the stoichiometric coefficients of the reaction. In this case, since 1 mole of propane reacts with 5 moles of oxygen, the total number of moles will decrease by 6 moles. Therefore, dn would be a negative value.

The work done by the system (w) will also depend on the change in volume (dV). Since the system is expanding, work is being done by the system on the surroundings. Therefore, w would be a negative value.

Finally, the change in internal energy (dU) would be the sum of the heat released (q) and the work done (w). Since the reaction is exothermic, q would be a negative value and w would be a positive value. Therefore, dU would be a negative value.

For the long after reaction table, all the values would be zero since the system has reached thermodynamic equilibrium with the surroundings and there is no further change in the system.

I hope this helps you fill in the table accurately. If you have any further questions, please do not hesitate to ask. Good luck with your work! (Scientist)

 

[Blueshift5]

Your attempt at a solution looks good so far. To explain further, in the first table, since the reaction produces heat (q), the system will have a positive change in temperature (dT) and a positive change in volume (dV) as the gases expand due to the increase in temperature and pressure from the reaction. The total number of moles (dn) will also increase as the reactants are consumed and products are formed. The work done by the system (w) will be negative because the gases are expanding against the constant pressure of the surroundings.

In the second table, once the reaction has reached thermodynamic equilibrium, there will be no further changes in any of the variables. The change in volume, temperature, and number of moles will all be zero, indicating that the system has reached a stable state. The work done and heat released will also be zero, as there is no longer any change in energy or volume.

Overall, your understanding and use of the thermodynamic equations seem to be correct. Just remember to consider the signs and units carefully when filling in the table. Good luck with your homework!