Calculus problem regarding Thermodynamics HW (entropy for C2H5OH at 348K)

I can figure it out. In summary, the conversation is about a student struggling to use an equation given to them to calculate the entropy for a substance at a certain temperature. The equation involves integrating and using specific heat capacity, but the student is having trouble understanding how to use it. They have been given a hint to break the integral into smaller parts.
  • #1
densephysicist
2
0
Summary:: Seems simple but has me stumped...

[Thread moved from a technical forum, so no Homework Template is shown]

Hello! I am struggling to use an equation given to me. To provide some context, I am trying to work out the entropy for C2H5OH at 348K.

Using provided tabulated data, the entropy (S) for C2H5OH at 298K is 160.7 [J/K].

I have also been given the specific heat capacity at constant pressure (111.46 [J/K]) and have been instructed to assume that it is independent of temp.

I simply cannot understand how to use the equation given to me...

S(T) = (integration sign with limits of 0 to T) Cp / T (derivative dash) * dT(deriv dash)

Any help is greatly appreciated.
 
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  • #2
densephysicist said:
Summary:: Seems simple but has me stumped...

[Thread moved from a technical forum, so no Homework Template is shown]

Hello! I am struggling to use an equation given to me

Hint:
$$\int_0^{T_2} = \int_0^{T_1} + \int_{T_1}^{T_2}$$
 
  • #3
Thanks George, I'll try to apply your hint
 

1. What is the formula for calculating entropy in a calculus problem involving thermodynamics?

The formula for calculating entropy is ΔS = qrev/T, where ΔS is the change in entropy, qrev is the reversible heat transfer, and T is the temperature in Kelvin.

2. How do I calculate the reversible heat transfer (qrev) in a calculus problem involving thermodynamics?

To calculate qrev, you will need to use the specific heat capacity (Cp) of the substance, the temperature change (ΔT), and the number of moles of the substance (n). The formula for qrev is qrev = nCpΔT.

3. Can you provide an example of a calculus problem involving thermodynamics and entropy?

Sure, here is an example: Calculate the change in entropy for the combustion of 2 moles of ethanol (C2H5OH) at 348K, assuming the reaction is reversible and the products are in their standard state. The standard enthalpy of formation for C2H5OH is -234.8 kJ/mol.

4. How do I convert temperature from Celsius to Kelvin in a calculus problem involving thermodynamics?

To convert from Celsius to Kelvin, simply add 273 to the Celsius temperature. In this case, the temperature of 348K is equivalent to 621K.

5. What units should I use for entropy in a calculus problem involving thermodynamics?

The SI unit for entropy is joules per Kelvin (J/K). However, in some cases, it may be more convenient to use kilojoules per Kelvin (kJ/K) or calories per Kelvin (cal/K).

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