To isolate \( T_c \) (the cold temperature) from the efficiency formula:

\[
\% \text{Eff} = \left( 1 - \frac{T_c}{T_h} \right) \times 100\%
\]

### Steps to isolate \( T_c \):

1. **Divide both sides by 100** to remove the percentage:
   \[
   \frac{\% \text{Eff}}{100} = 1 - \frac{T_c}{T_h}
   \]

2. **Subtract 1 from both sides**:
   \[
   \frac{\% \text{Eff}}{100} - 1 = - \frac{T_c}{T_h}
   \]

3. **Multiply both sides by -1** to get rid of the negative sign:
   \[
   1 - \frac{\% \text{Eff}}{100} = \frac{T_c}{T_h}
   \]

4. **Multiply both sides by \( T_h \)** to isolate \( T_c \):
   \[
   T_c = T_h \times \left( 1 - \frac{\% \text{Eff}}{100} \right)
   \]

Thus, the isolated formula for \( T_c \) is:

\[
T_c = T_h \times \left( 1 - \frac{\% \text{Eff}}{100} \right)
\]

Do you need any further clarification or details?

Here are 5 related questions to consider:
1. How does the efficiency of a heat engine depend on the temperature difference?
2. What would happen to the efficiency if \( T_h \) and \( T_c \) were very close?
3. How does an increase in \( T_h \) affect the value of \( T_c \)?
4. Can the efficiency ever be 100% according to this formula?
5. How does this formula relate to Carnot's theorem?

**Tip:** Efficiency formulas often assume absolute temperature in Kelvin for accurate calculations, so ensure you use the right units!

Learn how to isolate T_c (the cold temperature) in the efficiency formula % Eff = (1 - T_c / T_h) * 100%. Follow step-by-step instructions and examples to understand the calculation process. Suitable for advanced high school students and anyone interested in thermodynamics and percentage calculations.

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