Temperature: Videos & Practice Problems

Temperature is a measure of how hot or cold something is, related to the average kinetic energy of particles. The three main temperature scales are Fahrenheit, Celsius, and Kelvin. The freezing and boiling points of water serve as reference points: 0°C (32°F) and 100°C (212°F) for Celsius and Fahrenheit, respectively. The Kelvin scale starts at absolute zero (0 K), equivalent to -273.15°C. Key conversion equations include: $T$_F=95T_C+32 and $T$_C=59(T_F-32).

Introduction To Temperature Scales

Thermodynamics begins with the fundamental concept of temperature, which serves as a measure of how hot or cold an object is. A more precise definition relates temperature to the average kinetic energy of the particles within a substance. For instance, the molecules in an ice cube vibrate slowly, indicating low kinetic energy and thus a low temperature, while the molecules in boiling water move rapidly, reflecting high kinetic energy and a high temperature.

In physics, three primary temperature scales are utilized: Fahrenheit, Celsius, and Kelvin, each based on reproducible reference points related to water. The Fahrenheit scale, commonly used in the United States, defines the freezing point of water at 32 degrees Fahrenheit and the boiling point at 212 degrees Fahrenheit. Conversely, the Celsius scale, prevalent in most other parts of the world, sets the freezing point at 0 degrees Celsius and the boiling point at 100 degrees Celsius. It is important to note that these scales represent the same physical phenomena but use different numerical values, similar to how 12 inches equals 1 foot.

The Kelvin scale is particularly significant in scientific contexts as it is an absolute temperature scale, starting at absolute zero, the theoretical lowest temperature possible. Absolute zero is defined as 0 Kelvin, which corresponds to -273.15 degrees Celsius and -459.67 degrees Fahrenheit. The Kelvin scale is essential for calculations in thermodynamics, as it allows for a direct relationship between temperature and energy. The differences between the freezing and boiling points in both the Celsius and Kelvin scales are 100 units, while the difference in the Fahrenheit scale is 180 units, indicating a larger range of values within that scale.

Understanding these temperature scales and their relationships is crucial for further studies in thermodynamics, as they provide the foundation for measuring thermal energy and conducting related calculations.

How To Convert Between Temperature Units

In thermodynamics, understanding temperature conversions between different units—Fahrenheit, Celsius, and Kelvin—is essential. Each unit serves a specific purpose, and knowing how to convert between them is crucial for solving various problems. The conversion process is straightforward, relying on specific equations that relate these temperature scales.

When converting from Celsius to Fahrenheit, the formula used is:

$$ T_F = \frac{9}{5} T_C + 32 $$

Conversely, to convert from Fahrenheit to Celsius, the equation is rearranged to:

$$ T_C = \frac{5}{9} (T_F - 32) $$

For conversions between Celsius and Kelvin, the relationship is simpler since both scales have the same incremental change. The conversion from Celsius to Kelvin is given by:

$$ T_K = T_C + 273.15 $$

And to convert from Kelvin to Celsius, the formula is:

$$ T_C = T_K - 273.15 $$

When converting between Kelvin and Fahrenheit, the equations become a bit more complex. To convert from Kelvin to Fahrenheit, the formula is:

$$ T_F = \frac{9}{5} T_K - 459.67 $$

And to convert from Fahrenheit to Kelvin, the equation is:

$$ T_K = \frac{5}{9} (T_F + 459.67) $$

These equations can be derived from the relationships between the different temperature scales. For example, when converting from Celsius to Kelvin, you simply add 273.15, which accounts for the difference in the starting points of the two scales. It’s important to remember that Kelvin is an absolute scale, meaning it cannot have negative values, as it starts from absolute zero.

For practical application, consider converting -196 degrees Celsius to Kelvin. Using the equation:

$$ T_K = -196 + 273.15 = 77.15 \text{ K} $$

This result is positive, as expected for Kelvin. Now, if we want to convert -196 degrees Celsius to Fahrenheit, we use:

$$ T_F = \frac{9}{5} (-196) + 32 = -320.8 \text{ °F} $$

When expressing temperatures, remember that Fahrenheit is denoted with "degrees" (°F), while Kelvin is simply represented as "K" without the degree symbol. Mastering these conversions and understanding the relationships between the temperature scales will enhance your problem-solving skills in thermodynamics.

The tungsten filaments inside of most incandescent lightbulbs reach temperatures of about 4580°F when the lightbulbs are lit. What is this temperature in a) Celsius and b) Kelvin?

• A. a) 2527°C
  b) 2785 K
• B. a) 8276°C
  b) 8549 K
• C. a) 2527°C
  b) 2800 K
• D. a) 4853°C
  b) 2728 K

Answer: (C)

Converting Between Celsius and Fahrenheit

To find the temperature at which the Celsius and Fahrenheit scales are equal, we start by understanding the relationship between the two temperature scales. The conversion formula from Celsius (Tc) to Fahrenheit (Tf) is given by:

\( T_f = \frac{9}{5} T_c + 32 \)

We are looking for a temperature where \( T_c = T_f \). To simplify the problem, we can replace both variables with a single variable \( t \), leading to the equation:

\( t = \frac{9}{5} t + 32 \)

Next, we rearrange the equation to isolate \( t \). Subtracting \( \frac{9}{5} t \) from both sides gives:

\( t - \frac{9}{5} t = 32 \)

To combine the terms on the left, we convert \( t \) into a fraction with a common denominator:

\( \frac{5}{5} t - \frac{9}{5} t = 32 \)

This simplifies to:

\( -\frac{4}{5} t = 32 \)

To solve for \( t \), we multiply both sides by \( -\frac{5}{4} \):

\( t = 32 \times -\frac{5}{4} \)

Calculating this gives:

\( t = -40 \)

This means that at \( -40 \) degrees, both the Celsius and Fahrenheit scales are equal. To verify, we can substitute \( -40 \) back into the original conversion formula:

\( T_f = \frac{9}{5}(-40) + 32 = -40 \)

Thus, the magical temperature where Celsius and Fahrenheit are the same is indeed \( -40 \) degrees.

Here’s what students ask on this topic:

What is the definition of temperature in physics?

In physics, temperature is defined as a measure of how hot or cold something is. More precisely, it is related to the average kinetic energy of the particles that make up an object. The faster the particles move, the higher the temperature. For example, in a pot of boiling water, the water molecules move very quickly, indicating a high temperature. Conversely, in an ice cube, the molecules vibrate slowly, indicating a low temperature.

What are the three main temperature scales used in physics?

The three main temperature scales used in physics are Fahrenheit, Celsius, and Kelvin. The Fahrenheit scale is commonly used in the United States, with the freezing point of water at 32°F and the boiling point at 212°F. The Celsius scale, used worldwide, has the freezing point of water at 0°C and the boiling point at 100°C. The Kelvin scale, used in scientific contexts, starts at absolute zero (0 K), equivalent to -273.15°C, and is used for most thermodynamic calculations.

How do you convert Celsius to Fahrenheit?

To convert Celsius to Fahrenheit, you can use the following equation:

$T{F}_{}=\frac{9}{5}T{C}_{}+32$

For example, if you have a temperature of 25°C, you can convert it to Fahrenheit as follows:

$T{F}_{}=\frac{9}{5}\left(25\right)+32=77$

What is absolute zero?

Absolute zero is the lowest possible temperature, where the kinetic energy of particles is minimal. It is defined as 0 Kelvin (K), which is equivalent to -273.15°C or -459.67°F. At absolute zero, particles theoretically stop moving entirely, and no further thermal energy can be extracted from the substance. This concept is fundamental in thermodynamics and helps define the Kelvin temperature scale.

How do you convert Kelvin to Celsius?

To convert Kelvin to Celsius, you can use the following equation:

$T{C}_{}=T{K}_{}-273.15$

For example, if you have a temperature of 300 K, you can convert it to Celsius as follows:

$T{C}_{}=300-273.15=26.85$

Why is the Kelvin scale considered an absolute temperature scale?

The Kelvin scale is considered an absolute temperature scale because it starts at absolute zero, the lowest possible temperature where particles have minimal kinetic energy. Unlike the Celsius and Fahrenheit scales, which are based on arbitrary reference points like the freezing and boiling points of water, the Kelvin scale is based on a fundamental physical limit. This makes it particularly useful in scientific calculations and thermodynamics.