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.