Interactive heat and thermodynamics simulator
Temperature
Dive into the thermodynamics of temperature. Visualize molecular motion in a gas chamber, watch Celsius, Fahrenheit, and Kelvin liquid expansion side-by-side, and explore absolute zero.
Kinetic Theory & Calibration Simulator
Heat or cool the system to change temperature. Observe molecular speeds (kinetic theory) or watch liquid columns expand in Celsius, Fahrenheit, and Kelvin thermometers.
Live Lab Telemetry
- Celsius
- 25.0 °C
- Fahrenheit
- 77.0 °F
- Kelvin
- 298.15 K
- Avg Kinetic Energy
- 6.17 × 10²¹ J
- RMS Speed (v_rms)
- 1360 m/s
- Collision Rate
- 124 Hz
What is Temperature?
Macroscopically, temperature is a quantitative measurement of the degree of hotness or coldness of an object. It represents a fundamental state variable of matter that dictates the direction of net heat flow. When two objects are in thermal contact, thermal energy transfers spontaneously from the body at the higher temperature to the body at the lower temperature until thermal equilibrium is established.
Microscopically, temperature is a direct manifestation of the random motion of atoms and molecules. According to the kinetic theory of gases, gas molecules are in constant, chaotic, translational motion. The absolute temperature of a gas is directly proportional to the average translational kinetic energy of its constituent particles. The relationship is expressed as:
where \(k_B\) is the Boltzmann constant (\(1.38 \times 10^{-23}\text{ J/K}\)) and \(T\) is the absolute temperature in Kelvin. This implies that at absolute zero (\(0\text{ K}\)), the random translational kinetic energy classically drops to zero.
Zeroth Law & Thermometry
The Zeroth Law of Thermodynamics states that if system A is in thermal equilibrium with system B, and B is in thermal equilibrium with system C, then A and C are in thermal equilibrium with each other. This transitive relationship allows us to define temperature scales and calibrate thermometers.
- Thermal equilibrium means no net heat flows.
- Thermometers act as "system B" to compare temperatures.
- Thermal expansion is the most common thermometric property.
Temperature Conversions
\(T_{\text{Kelvin}} = T_{\text{Celsius}} + 273.15\)
\(T_{\text{Fahrenheit}} = \frac{9}{5} T_{\text{Celsius}} + 32\)
\(T_{\text{Celsius}} = \frac{5}{9} (T_{\text{Fahrenheit}} - 32)\)
Comparison of Scales
| Reference Point | Kelvin (K) | Celsius (°C) | Fahrenheit (°F) |
|---|---|---|---|
| Absolute Zero | 0 K | -273.15 °C | -459.67 °F |
| Water Freezing | 273.15 K | 0 °C | 32 °F |
| Room Temp | 298.15 K | 25 °C | 77 °F |
| Water Boiling | 373.15 K | 100 °C | 212 °F |
Microscopic Motion
In a gas, molecules collide elastically. The root-mean-square speed \(v_{\text{rms}}\) represents the typical speed of a gas particle, which increases with temperature:
Where \(R\) is the ideal gas constant (\(8.314\text{ J/(mol·K)}\)) and \(M\) is the molar mass of the gas.
Solved Examples
Convert normal human body temperature, which is approximately 37°C, to Fahrenheit and Kelvin.
- To convert Celsius to Fahrenheit, use: \(T_F = \frac{9}{5} T_C + 32\).
- Substitute \(T_C = 37\): \(T_F = \frac{9}{5}(37) + 32 = 66.6 + 32 = 98.6^\circ\text{F}\).
- To convert Celsius to Kelvin, use: \(T_K = T_C + 273.15\).
- Substitute \(T_C = 37\): \(T_K = 37 + 273.15 = 310.15\text{ K}\).
Answer: Body Temperature = 98.6°F = 310.15 K
At what temperature do the Celsius and Fahrenheit scales read the exact same numerical value?
- Set the Celsius and Fahrenheit temperatures equal to each other: \(T_C = T_F = x\).
- Use the conversion formula: \(T_F = \frac{9}{5} T_C + 32\).
- Substitute \(x\): \(x = \frac{9}{5}x + 32\).
- Subtract \(\frac{9}{5}x\) from both sides: \(-\frac{4}{5}x = 32\).
- Solve for \(x\): \(x = 32 \times \left(-\frac{5}{4}\right) = -40\).
Answer: Numerical crossing point = -40°C = -40°F
Calculate the average kinetic energy (in Joules) of a Helium gas molecule at room temperature (27°C). (Boltzmann constant \(k_B = 1.38 \times 10^{-23}\text{ J/K}\))
- First, convert the temperature from Celsius to Kelvin: \(T = 27 + 273.15 = 300.15\text{ K}\).
- The average kinetic energy of a molecule is given by: \(E_k = \frac{3}{2} k_B T\).
- Substitute the values: \(E_k = 1.5 \times (1.38 \times 10^{-23}\text{ J/K}) \times 300.15\text{ K}\).
- Calculate: \(E_k = 2.07 \times 10^{-23} \times 300.15 \approx 6.21 \times 10^{-21}\text{ J}\).
Answer: Average Kinetic Energy = 6.21 × 10-21 J
Common Mistakes
- Writing "degree Kelvin" (e.g. 100°K). Kelvin is an absolute unit and should be written as 100 K.
- Forgetting to convert temperatures to Kelvin when using the Ideal Gas Law or kinetic equations.
- Confusing heat (thermal energy transferred) with temperature (average kinetic energy of particles).
- Assuming negative temperatures exist on the Kelvin scale. Absolute zero is the lowest limit.
Practice Questions
1. What does temperature measure on a microscopic level?
It measures the average translational kinetic energy of the individual particles (atoms or molecules) in a substance. Higher temperature means faster chaotic movement.
2. Liquid nitrogen boils at 77 K. What is this temperature in Celsius?
Using \(T_C = T_K - 273.15\), we get \(T_C = 77 - 273.15 = -196.15^\circ\text{C}\).
3. Explain the Zeroth Law of Thermodynamics and its significance.
It states that if two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This allows us to define and measure temperature using thermometers.
4. If a gas is cooled to absolute zero, what happens to the motion of its particles?
Classically, all molecular motion would stop completely. Quantum mechanically, particles still possess a tiny, minimum vibrational energy called zero-point energy, but all heat-driven random motion ceases.
Quick Summary
- Temperature is the average kinetic energy of random particle movement inside a substance.
- Heat is the transfer of thermal energy from higher to lower temperature bodies.
- Celsius and Fahrenheit are relative scales, while Kelvin is the absolute scale.
- Thermometers rely on thermal equilibrium and the expansion of thermometric fluids.
- At 0 K (absolute zero), thermal particle motion reaches its classical minimum.
Frequently Asked Questions
What is temperature in simple terms?
Temperature is a measure of how hot or cold something is. It determines which way heat will flow when two objects touch—heat always moves from the hotter object to the colder one.
What is the difference between heat and temperature?
Heat is the total thermal energy transferred between substances (dependent on mass and material), while temperature is the average kinetic energy of individual particles (independent of mass).
How does a traditional thermometer work?
It works on the principle of thermal expansion. Most materials expand when heated. Liquid thermometers contain mercury or alcohol that expands up a narrow tube when temperature rises.
What is the Kelvin scale?
The Kelvin scale is the SI absolute temperature scale. It starts at absolute zero (0 K), the coldest possible temperature, so it has no negative numbers.
Why do we use Kelvin in physics calculations?
Because Kelvin is directly proportional to molecular kinetic energy. Using Celsius or Fahrenheit in gas laws (like PV = nRT) would cause errors because their zero points are arbitrary.
What is absolute zero in Celsius and Fahrenheit?
Absolute zero is -273.15°C or -459.67°F. It is the temperature at which all random thermal motion of particles stops.
Can we reach absolute zero in a laboratory?
No. According to the Third Law of Thermodynamics, it is impossible to reach absolute zero in a finite number of steps, though scientists have cooled atoms to less than a billionth of a degree above it.
What is thermal equilibrium?
It is the state reached when two objects in thermal contact stop exchanging heat because they have reached the exact same temperature.
What are the freezing and boiling points of water on all three scales?
Celsius: 0°C and 100°C. Fahrenheit: 32°F and 212°F. Kelvin: 273.15 K and 373.15 K.
How does thermal energy relate to temperature?
Thermal energy is the total internal kinetic energy of all particles in an object. Temperature is the average kinetic energy. For example, a cup of tea can be the same temperature as a swimming pool, but the swimming pool has much more thermal energy.