Question

What pressure is exerted by an ideal gas at absolute zero?

Short answer

The pressure exerted is 0 atm at absolute zero.

Step-by-step solution

Understanding the Ideal Gas Law

The ideal gas law is given by the formula \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Substituting Absolute Zero into the Formula

Absolute zero is the lowest possible temperature, equal to 0 Kelvin. Substituting \( T = 0 \) into the ideal gas law formula: \( PV = nR(0) \).

Simplifying the Equation

When the term \( nR(0) \) is calculated, it results in zero. Therefore, the equation simplifies to \( PV = 0 \).

Concluding the Pressure Calculation

To find the pressure \( P \), rearrange the equation: \( P = \frac{0}{V} \). Since any number divided by a positive non-zero number (volume \( V \) cannot be zero) results in zero, the pressure \( P \) exerted by the gas is 0 atm.

Key concepts

Absolute Zero

The concept of absolute zero is fascinating, and it plays a critical role in understanding the behaviors of gases. Imagine a temperature so cold that molecular motion practically comes to a halt. This theoretical temperature is known as absolute zero. At absolute zero, which is precisely 0 Kelvin (-273.15°C), atoms are at their lowest energy state. In this state, they have minimal vibrational motion. Absolute zero represents the very bottom of the thermodynamic temperature scale. Understanding this concept helps us comprehend why certain phenomena occur, such as the disappearance of gas pressure as the temperature approaches absolute zero. By knowing about absolute zero, you can better grasp the intricacies behind temperature's influence on the physical properties of matter.

Pressure Calculation

Calculating pressure in gases requires a good understanding of the Ideal Gas Law. Pressure is essentially the force exerted by gas molecules as they collide with the walls of their container. This force can be calculated using the equation: \[ PV = nRT \] Each variable in this formula has a specific role: - **P** stands for pressure, typically measured in atmospheres (atm).- **V** represents volume, commonly in liters.- **n** indicates the amount of gas in moles.- **R** is the ideal gas constant, with a value of 0.0821 L·atm/mol·K.- **T** signifies the temperature in Kelvin.When substituting absolute zero into this formula ( T = 0 ), the calculation simplifies to zero force. Hence, at absolute zero, the pressure also corresponds to zero. It's vital to note that this is a theoretical concept because reaching absolute zero is practically impossible with our current technology. Yet, this calculation showcases how profoundly temperature impacts pressure.

Kelvin Temperature Scale

The Kelvin temperature scale is crucial when dealing with thermodynamics and gas calculations. Unlike Celsius or Fahrenheit, Kelvin begins at absolute zero, providing a direct relationship to the physical properties of gases. Some of the main features of the Kelvin scale include:

• It is an absolute scale starting from zero, which represents the absence of thermal energy.
• Whenever dealing with thermodynamic equations like the Ideal Gas Law, temperatures must be in Kelvin to ensure accuracy.
• The size of a Kelvin is the same as a degree Celsius, meaning it's easy to convert: add 273.15 to a Celsius temperature to convert it to Kelvin.

Using Kelvin helps scientists ensure that calculations are consistent and avoid negative temperature values, which could lead to incorrect interpretations of physical phenomena.