An equation that describes the maximum and minimum temperatures at which a chemical compound is in a liquid state is given by the absolute value equation I T - 50 I = 50, where T is the temperature in degrees Celsius. Calculate the range in temperature, and identify the chemical compound.
To calculate the range in temperature for the given equation, we can solve for T by isolating T on one side of the equation. Let's break down the steps:
1. Start with the absolute value equation: |T - 50| = 50.
2. Since the absolute value of a number is equal to that number or its negation, we can write two separate equations to consider both cases:
a) T - 50 = 50
b) -(T - 50) = 50
3. Solve equation (a) for T:
T - 50 = 50
T = 50 + 50
T = 100
4. Solve equation (b) for T:
-(T - 50) = 50
-T + 50 = 50
-T = 50 - 50
-T = 0
T = 0
Now we have two possible values for T: T = 0 and T = 100.
The chemical compound will be in a liquid state within the range of temperatures covered by these two solutions. Therefore, the range in temperature is from 0 degrees Celsius to 100 degrees Celsius.
However, it's important to note that these solutions may not provide the complete range of temperatures for which the chemical compound exists in a liquid state. The given equation only represents a theoretical scenario, and additional information and experimental data are required to identify the specific chemical compound.