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 |T - 50 |= 50, where T is the temperature in degrees Celsius. Calculate the range in temperature, and identify the chemical compound.
T - 50 = 50 ... T = 100
T - 50 = -50 ... T = 0
liquid between 0ºC and 100ºC ... looks like water ...H2O
To calculate the range in temperature and identify the chemical compound, let's solve the absolute value equation step-by-step.
Step 1: Start with the given equation |T - 50| = 50.
Step 2: Split the equation into two separate equations, one with the positive value and one with the negative value:
a) T - 50 = 50,
b) T - 50 = -50.
Step 3: Solve equation (a) for T:
T - 50 = 50,
T = 50 + 50,
T = 100.
Step 4: Solve equation (b) for T:
T - 50 = -50,
T = -50 + 50,
T = 0.
So, the two solutions for T are T = 100 and T = 0.
Step 5: Calculate the range in temperature by subtracting the smaller value from the larger value:
Range = 100 - 0,
Range = 100.
Therefore, the range in temperature is 100 degrees Celsius.
Step 6: To identify the chemical compound, we need more information. The equation provided defines the temperature range at which the compound is in a liquid state, but it does not specify the compound itself. Additional information is required to determine the identity of the chemical compound.
To calculate the range in temperature, we need to solve the absolute value equation:
|T - 50| = 50
To solve this equation, we can break it down into two separate equations:
1) T - 50 = 50
2) -(T - 50) = 50
Solving equation 1:
T - 50 = 50
Adding 50 to both sides:
T = 100
Solving equation 2:
-(T - 50) = 50
Expanding the negative:
-T + 50 = 50
Subtracting 50 from both sides:
-T = 0
Multiplying by -1:
T = 0
So, the solutions to the absolute value equation are T = 100 and T = 0.
The range in temperature can be found by subtracting the smaller value from the larger value:
Range = 100 - 0 = 100 degrees Celsius.
Now, to identify the chemical compound, we need more information. The equation given describes the maximum and minimum temperatures at which the compound is in a liquid state, but we don't have enough information to determine the specific compound.