Question

One thermometer is calibrated in degrees Celsius, and another in degrees Fahrenheit. At what temperature is the reading on the thermometer calibrated in degrees Celsius three times the reading on the other thermometer?

Short answer

Answer: 20°C (68°F)

Step-by-step solution

Write down the temperature relationship between Celsius and Fahrenheit

The formula describing the relationship between Celsius and Fahrenheit temperatures is given by: °F = (9/5)*°C + 32

Set up the equation for the problem

According to the problem, the Celsius reading is three times the Fahrenheit reading. So, we will set up the equation as follows: °C = 3 × °F Now we will substitute the Fahrenheit temperature from the Celsius equation into this equation: °C = 3 × ((9/5)*°C + 32)

Solve the equation for °C

Next, we need to solve the equation for the Celsius temperature. To solve it, we will first distribute the 3 and combine like terms: °C = (27/5)*°C + 96 Now, subtract (27/5)*°C from both sides of the equation: (1 - 27/5)*°C = 96 (-22/5)*°C = 96 To isolate °C, we will divide both sides by (-22/5): °C = 96 / (-22/5) = (-22/5) * (-5/22) * 96 = 20 So the temperature in Celsius is 20°C.

Convert the temperature back to Fahrenheit

Finally, we need to convert the temperature in Celsius back to Fahrenheit. We will use the relationship between Celsius and Fahrenheit: °F = (9/5)*°C + 32 °F = (9/5)*20 + 32 °F = 36 + 32 °F = 68 So the temperature in Fahrenheit is 68°F. Therefore, at a temperature of 20°C (68°F), the reading on the thermometer calibrated in degrees Celsius is three times the reading on the other thermometer.

Key concepts

Celsius and Fahrenheit relationship

The relationship between Celsius and Fahrenheit is a fundamental concept in temperature conversion. These two units are standard in different parts of the world: Celsius is primarily used in scientific contexts and most countries, while Fahrenheit is mainly used in the United States. Understanding how to convert between them is crucial for scientific calculations and everyday life.

The formula to convert Celsius (°C) to Fahrenheit (°F) is:

• °F = (9/5) × °C + 32

This equation reveals the difference in zero points and the scaling factors of both units.

The Conversion Process:
The formula consists of two key operations:

• Multiplication by 9/5, which accounts for the differences in degree size between the scales.
• Adding 32, which aligns the zero points, as 0°C corresponds to 32°F, the freezing point of water in both units.

Thus, when you're working with temperature problems involving these units, it helps to memorize and understand this formula. Once you're familiar with it, you can easily switch between Celsius and Fahrenheit and tackle various thermometry tasks.

thermometer calibration

Calibrating thermometers is a crucial process to ensure their accuracy and reliability when measuring temperature. Calibration involves adjusting and verifying the instrument to align with established standards or known temperature values.

Why Calibration Matters:

• Ensures that readings are precise and consistent over time.
• Prevents measurement errors that can lead to incorrect conclusions and decisions, especially in scientific and industrial applications.
• Maintains quality control if thermometers are used in manufacturing processes or medical settings.

Calibration Process:
The basic steps usually involve:

• Comparing the thermometer's reading to a known reference temperature, such as the melting point of ice or the boiling point of water.
• Adjusting the instrument if there is any deviation from the expected reading.
• Periodic recalibration to account for any wear and tear that might affect accuracy over time.

Through proper calibration, thermometers can provide accurate readings, essential for experiments, culinary tasks, and environmental monitoring.

mathematical equations in physics

Mathematical equations are the backbone of physics, articulating physical laws and concepts in a precise and computational form. They provide a framework for analyzing real-world phenomena, predicting outcomes, and solving practical problems.

The Role of Equations:

• Equations simplify complex relationships into manageable forms.
• They link multiple variables, allowing exploration of "what if" scenarios by adjusting these parameters.
• Facilitate the conversion of theoretical ideas into quantifiable expressions that can be tested and verified through experiments.

Solving Physics Problems:
When faced with a physics problem, breaking it down using equations is critical:

• Identify known and unknown quantities, often given in the problem statement.
• Select the appropriate equation or set of equations that capture the relevant physical principles.
• Solve algebraically, step by step, ensuring dimensional consistency and calculation accuracy.

Physics equations, like the ones used for temperature conversion, make it feasible to move seamlessly between theoretical understanding and practical application, highlighting the elegance and utility of mathematics in science.