How does the pressure exerted by an ideal gas change as it approaches absolute zero at constant volume?

The pressure decreases linearly with temperature and theoretically reaches zero at absolute zero. This occurs because pressure is caused by molecular collisions, which cease when kinetic energy becomes zero.

When comparing a change of $10 \text{ K}$ to a change of $10 \text{ °C}$, which interval is larger?

The intervals are exactly the same size. The Kelvin and Celsius scales use the same unit magnitude for temperature increments, differing only in their starting (zero) points.

What is the difference between the zero points of the Celsius and Kelvin scales?

The Celsius scale is zeroed at the freezing point of water, whereas the Kelvin scale is zeroed at absolute zero. Consequently, $0 \text{ °C}$ corresponds to $273 \text{ K}$.

Why is it incorrect to state that a gas has a temperature of $-50 \text{ K}$?

Absolute zero ($0 \text{ K}$) is the lowest possible energy state where kinetic energy is zero. Since kinetic energy cannot be negative, temperatures below $0 \text{ K}$ are physically impossible.

What common mistake do students make when using the Pressure Law ($P_1/T_1 = P_2/T_2$)?

Students often use Celsius temperatures instead of Kelvin. These laws are based on absolute ratios, so failure to convert to Kelvin leads to mathematically incorrect results.

If a gas temperature increases from $20 \text{ °C}$ to $40 \text{ °C}$, has the average kinetic energy doubled?

No, because kinetic energy is proportional to the absolute temperature in Kelvin. The temperature actually rose from $293 \text{ K}$ to $313 \text{ K}$, which is a much smaller fractional increase than doubling.

Define Absolute Zero in terms of kinetic energy.

Absolute zero is the temperature at which the average kinetic energy of the molecules in a substance is zero. At this point, all random molecular motion stops.

What is the specific value of absolute zero on the Celsius scale?

Absolute zero is equal to $-273 \text{ °C}$. This value is determined by extrapolating the linear relationship between gas pressure and temperature back to zero pressure.

State the formula used to convert a Celsius temperature ($\theta$) to a Kelvin temperature ($T$).

The conversion formula is $T = \theta + 273$. This adds the offset required to shift from the freezing point of water to the absolute zero reference point.

Why does the pressure of a gas drop to zero at absolute zero?

Pressure is the result of particle collisions with the walls of a container. Since particles have zero kinetic energy at absolute zero, they stop moving and stop colliding, thus exerting no pressure.

Library Podcasts

Courses

Referral & Rewards

5. Solids, Liquids & Gases

Absolute Zero

Summary

Absolute zero represents the theoretical lower limit of thermodynamic temperature, where the internal energy of a system reaches its minimum. At this state, molecular motion effectively ceases, resulting in zero kinetic energy and zero pressure exerted by a gas.

1. Definition & Core Concepts

Absolute Zero: This is defined as the lowest possible temperature where the molecules of a substance have zero kinetic energy. It is the point at which all thermal motion in a system stops entirely.
Numerical Values: On the Celsius scale, absolute zero is exactly $-273.15 \text{ °C}$ (often rounded to $-273 \text{ °C}$ for introductory physics), while on the thermodynamic scale, it is defined as $0 \text{ K}$ .
Absence of Negative Values: Because the Kelvin scale starts at absolute zero, it is physically impossible to have a negative temperature in Kelvin, as there is no state with less energy than zero kinetic energy.

Graph showing gas pressure decreasing linearly with temperature, extrapolating to zero pressure at -273 degrees Celsius.

2. Underlying Principles

Kinetic Theory Basis: Temperature is a macroscopic measure of the average kinetic energy of microscopic particles. As energy is removed from a system, particle velocity decreases, leading to lower temperatures.
Pressure Generation: In a gas, pressure arises from particles colliding with container walls. At absolute zero, particles have no velocity and therefore cannot collide, resulting in the total absence of gas pressure.
Thermodynamic Limits: Absolute zero represents the state of minimum internal energy. It is considered an asymptotic limit; while scientists can get extremely close to it, reaching it exactly remains physically impossible due to quantum mechanical constraints.

3. The Kelvin Temperature Scale

4. Temperature Conversions

5. Key Distinctions

6. Exam Strategy & Tips