The correct option for the question regarding which factor primarily affects the electrical conductivity of gases at low pressures is **A. Temperature**. ### Detailed Explanation 1. **Understanding Electrical Conductivity in Gases**: - Electrical conductivity in gases refers to the ability of a gas to conduct electric current. This property is significantly influenced by the presence of charged particles (ions and electrons) in the gas. - At low pressures, gases are less dense, and the mean free path (the average distance a particle travels before colliding with another particle) increases. This means that the behavior of the gas can change significantly with variations in temperature. 2. **Role of Temperature**: - **Kinetic Energy**: As temperature increases, the kinetic energy of gas molecules also increases. This leads to more frequent and energetic collisions between gas molecules, which can result in the ionization of some molecules. - **Ionization**: Higher temperatures can provide enough energy to overcome the ionization energy of the gas molecules, creating more free electrons and positive ions. This increase in charged particles enhances the gas's ability to conduct electricity. - **Thermal Excitation**: At elevated temperatures, more molecules can be excited to higher energy states, which can also contribute to increased ionization and conductivity. 3. **Why Other Options Are Weaker**: - **B. Humidity**: While humidity can affect the conductivity of gases, especially in the context of air (where water vapor can ionize and contribute to conductivity), it is not the primary factor at low pressures. The effect of humidity is more pronounced in the presence of water vapor, but it does not fundamentally change the conductivity of the gas itself as temperature does. - **C. Ionization Energy**: Ionization energy is a property of the gas molecules themselves and determines how easily they can be ionized. However, it does not change with pressure or temperature. While it is a factor in determining how conductive a gas can be, it does not primarily affect conductivity at low pressures. - **D. Density of the Gas**: At low pressures, the density of the gas decreases, which can affect the number of collisions between particles. However, the primary factor influencing conductivity is the presence of free charge carriers, which is more directly influenced by temperature than by density. ### Formulas and Concepts - **Conductivity (σ)**: The electrical conductivity of a gas can be expressed as: \[ \sigma = n \cdot q \cdot \mu \] where: - \( n \) = number density of charge carriers (ions/electrons) - \( q \) = charge of the carriers - \( \mu \) = mobility of the charge carriers (which is influenced by temperature) - **Mean Free Path**: The mean free path (\( \lambda \)) is given by: \[ \lambda = \frac{kT}{\sqrt{2} \pi d^2 P} \] where: - \( k \) = Boltzmann's constant - \( T \) = absolute temperature - \( d \) = diameter of gas molecules - \( P \) = pressure ### Common Pitfalls - Students may confuse the effects of humidity and temperature, thinking that humidity is the primary factor affecting conductivity. It is essential to recognize that while humidity can influence conductivity, temperature has a more significant and direct impact on the ionization processes in gases. - Misunderstanding the role of ionization energy can lead to the incorrect assumption that it is a variable factor affecting conductivity, rather than a fixed property of the gas. ### Revision Summary - **Temperature** is the primary factor affecting the electrical conductivity of gases at low pressures due to its influence on kinetic energy and ionization. - Increased temperature leads to more free charge carriers, enhancing conductivity. - Humidity, ionization energy, and gas density play roles but are not the primary factors at low pressures. - Understanding the relationship between temperature and conductivity is crucial for analyzing gas behavior in electrical applications.