A 125 mL sample of water at 293.2 K was heated for 8 min, 25 s so as to give a constant temperature increase of 3.0 °F/min. What is the final temperature of the water in degrees Celsius?

Verified step by step guidance

1. Convert the temperature increase from degrees Fahrenheit per minute to degrees Celsius per minute using the conversion formula: \( \Delta T(\degree C) = \frac{5}{9} \times \Delta T(\degree F) \).
2. Calculate the total temperature increase in degrees Fahrenheit by multiplying the rate of temperature increase (3.0 \( \degree F/min \)) by the total time in minutes (8 minutes and 25 seconds).
3. Convert the total temperature increase from degrees Fahrenheit to degrees Celsius using the conversion formula from step 1.
4. Add the temperature increase in degrees Celsius to the initial temperature of the water, which is 293.2 K. First, convert 293.2 K to degrees Celsius using the formula: \( T(\degree C) = T(K) - 273.15 \).
5. Calculate the final temperature in degrees Celsius by adding the converted initial temperature in degrees Celsius to the temperature increase in degrees Celsius.

Key Concepts

Temperature Conversion

Understanding how to convert temperatures between different scales is essential. In this case, the temperature increase is given in degrees Fahrenheit, which must be converted to degrees Celsius using the formula: °C = (°F - 32) × 5/9. This conversion is crucial for accurately determining the final temperature in Celsius.

Heat Transfer and Specific Heat

The concept of heat transfer involves the movement of thermal energy from one object to another. In this scenario, the water absorbs heat, leading to a temperature increase. The specific heat capacity of water, which is approximately 4.18 J/g°C, indicates how much energy is required to raise the temperature of a given mass of water by one degree Celsius, although it is not directly needed for this calculation.

Rate of Temperature Change

The rate of temperature change describes how quickly the temperature of a substance increases over time. In this question, the water's temperature increases at a constant rate of 3.0 °F/min. To find the total temperature increase over the heating period, this rate must be multiplied by the total time in minutes, allowing for the calculation of the final temperature.