#### cryptoguy

When to use Q=n*Cp*ln(T2/T1) and when to use Q=n*Cp*Delta T? Is it something to do with the reversible process?

(I know Cp is specific heat capacity at constant pressure)

#### CParsons

Staff member
When to use Q=n*Cp*ln(T2/T1) and when to use Q=n*Cp*Delta T? Is it something to do with the reversible process?

(I know Cp is specific heat capacity at constant pressure)

I asked ChatGPT for you lol.

The two formulas you mentioned are different ways to express the heat transfer in a thermodynamic process, and they are both derived from the first law of thermodynamics. The choice between them depends on the specific information you have about the process.

1. **Q = n * Cp * ln(T2/T1):**
- This formula is based on the equation $$Q = \Delta U + W$$, where $$Q$$ is the heat transfer, $$\Delta U$$ is the change in internal energy, and $$W$$ is the work done. For a constant pressure process, $$Q$$ is approximately equal to $$n * Cp * \Delta T$$, where $$Cp$$ is the heat capacity at constant pressure.
- The ln(T2/T1) term arises when integrating the expression for $$Cp$$ with respect to temperature.

2. **Q = n * Cp * ΔT:**
- This formula is a simplified version that assumes constant heat capacity ($$Cp$$) over the temperature range of interest. It's applicable when $$Cp$$ is constant, and the temperature change ($$ΔT$$) is relatively small.
- This formula is often used for quick calculations or when the temperature range is not too large, and the heat capacity can be considered approximately constant.

In summary, use the formula that is most appropriate for the specific conditions of the process you are analyzing. If $$Cp$$ is constant and the temperature change is small, you can use $$Q = n * Cp * ΔT$$. If $$Cp$$ varies significantly with temperature, or if you need a more accurate representation, use $$Q = n * Cp * \ln(T2/T1)$$.

Miles

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