How Can I Accurately Calculate The Change In Internal Energy Of A System When It Undergoes A Thermodynamic Process Involving Both Isobaric And Isothermal Changes, Taking Into Account The Specific Heat Capacities Of The Substances Involved And The Work Done On Or By The System During The Process?

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The change in internal energy (ΔU) of a system undergoing a thermodynamic process involving both isobaric and isothermal changes can be accurately calculated by focusing on the overall temperature change, as internal energy is a state function dependent solely on temperature for an ideal gas. Here's the step-by-step approach:

  1. Identify Initial and Final States: Determine the initial temperature (T₁) and final temperature (T₂) of the system.

  2. Calculate Temperature Change: Compute the overall temperature change ΔT = T₂ - T₁.

  3. Apply the Formula: Use the formula ΔU = nCvΔT, where:

    • n = number of moles of the substance.
    • Cv = molar specific heat capacity at constant volume.
    • ΔT = temperature change.

  4. Sum Changes for Multiple Substances (if applicable): If the system involves multiple substances, calculate ΔU for each and sum them.

Thus, the total change in internal energy is determined by the overall temperature change and the specific heat capacity at constant volume.

Answer: The change in internal energy is given by ΔU = nCvΔT, where ΔT is the overall temperature change between the initial and final states.