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To solve this problem, let's break down the given information and apply the principles of thermal equilibrium and temperature conversions.

### Given Information
1. **Initial temperature of substance A** (\( T_{\text{hoog}} \)) in Fahrenheit:
   \[
   a = 109^\circ \text{F}
   \]
2. **Temperature change for substance A** in Celsius:
   \[
   \Delta T = b = -8^\circ \text{C}
   \]
3. **Temperature change for substance B** in Kelvin:
   \[
   \Delta T = c = 46 \text{ K}
   \]

The goal is to **find the initial temperature of substance B** in degrees Celsius.

### Solution
Since substances A and B reach thermal equilibrium, their final temperatures are equal. Let \( T_f \) represent this final temperature.

#### Step 1: Convert the Initial Temperature of Substance A to Celsius
Since \( a = 109^\circ \text{F} \), we convert this to Celsius using the formula:
\[
T_{\text{C}} = \frac{5}{9} (T_{\text{F}} - 32)
\]
Substituting \( T_{\text{F}} = 109 \):
\[
T_{\text{C}} = \frac{5}{9} (109 - 32) = \frac{5}{9} \times 77 = 42.78^\circ \text{C}
\]
Thus, the initial temperature of substance A in Celsius is approximately \( 42.78^\circ \text{C} \).

#### Step 2: Calculate the Final Temperature in Celsius
Substance A cools by \( b = -8^\circ \text{C} \), so:
\[
T_f = 42.78 + (-8) = 34.78^\circ \text{C}
\]

#### Step 3: Determine the Initial Temperature of Substance B
We know substance B heats up by \( c = 46 \) K. Since a change of 1 K is equivalent to a change of 1 °C, the temperature increase for B is also \( 46^\circ \text{C} \).

Let \( x \) represent the initial temperature of substance B in Celsius. Then:
\[
x + 46 = T_f
\]
\[
x + 46 = 34.78
\]
Solving for \( x \):
\[
x = 34.78 - 46 = -11.22^\circ \text{C}
\]

### Answer
The initial temperature of substance B is approximately:
\[
x = -11.22^\circ \text{C}
\]

---

Would you like a more detailed breakdown or explanation of any steps?

### Related Questions
1. How do you convert temperatures between Fahrenheit and Celsius accurately?
2. What are the principles of thermal equilibrium and how do they apply to this problem?
3. How do temperature changes in Kelvin compare to changes in Celsius?
4. What happens to the temperature of substances in thermal contact over time?
5. How does the specific heat of a substance affect its temperature change in thermal equilibrium?

### Tip
Remember, changes in temperature in Kelvin and Celsius are numerically the same (1 K = 1 °C), which is useful when calculating thermal equilibrium problems.

Als je 2 stoffen A en B in contact brengt met elkaar, zal de warmste stof warmte-energie doorgeven aan de koudste stof, tot ze uiteindelijk in thermisch evenwicht zijn (en allebei dezelfde eindtemperatuur hebben).

Je weet in dit geval (zie figuur):
1. dat de begintemperatuur van de warmste stof A gelijk is aan a = 109 °F
2. dat die stof zal afkoelen met ΔT = b = -8 °C
3. de koudste stof B zal opwarmen met ΔT = c = 46 K

Bereken de begintemperatuur van stof B, uitgedrukt in °C.

Learn how to calculate the initial temperature of substance B in a thermal equilibrium problem, given specific temperature changes and initial values. This solution involves converting Fahrenheit to Celsius and applying principles of thermal equilibrium. Suitable for students in Grades 10-12.

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