Question

Pressure of an ideal gas is increased by keeping temperature constant what is the effect on kinetic energy of molecules. (A) Decrease (B) Increase (C) No change (D) Can't be determined

Short answer

(C) No change

Step-by-step solution

Recall the Ideal Gas Law.

The Ideal Gas Law is given by the equation \[PV = nRT\], where: - P = pressure - V = volume - n = number of moles - R = universal gas constant - T = temperature Since we know that the temperature remains constant, we can examine the effects of pressure and volume on the equation.

Understand the relationship between pressure and volume.

As the pressure of the gas increases, the volume of the gas will decrease if the temperature remains constant (as per the problem statement). This is because the Ideal Gas Law equation shows that \(PV = \text{constant}\), when temperature is held constant.

Recall the formula for the average kinetic energy of gas molecules.

The formula for the average kinetic energy \(\overline{KE}\) of gas molecules can be written as \[\overline{KE} \propto T\], where proporitional sign (\(\propto\)) indicates that the average kinetic energy of the gas molecules is directly proportional to the temperature of the gas.

Determine the effect of increasing pressure on the kinetic energy of gas molecules.

From Steps 1 to 3, we learned that: 1. The temperature is held constant. 2. The average kinetic energy of the gas molecules is directly proportional to the temperature of the gas. Since the temperature remains constant, the average kinetic energy of the gas molecules will also remain constant (no change). Therefore, the correct answer is: (C) No change

Key concepts

Kinetic Energy of Gas Molecules

The kinetic energy of gas molecules is an important concept in understanding the behavior of gases. In the context of the ideal gas law, the average kinetic energy of gas molecules is directly linked to the temperature of the gas. This is expressed through the equation:

• Average Kinetic Energy ( \( \overline{KE} \) ) is directly proportional to temperature ( \( T \) ).

When we say that the kinetic energy is proportional to the temperature, we mean that if the temperature increases, the kinetic energy of molecules also increases. Conversely, if the temperature decreases, the kinetic energy decreases. Temperature provides a measure of how energetically molecules of a substance are moving.

In the scenario where we keep the temperature constant, it implies that no matter what changes occur in pressure or volume, the kinetic energy of the gas molecules will not change. This is because the kinetic energy is solely dependent on temperature. Thus, in situations where the temperature remains unchanged as described in the original exercise, the kinetic energy remains constant.

Pressure-Volume Relationship

The pressure-volume relationship is one of the cornerstones of understanding gas behavior, specifically described in Boyle's Law. When dealing with an ideal gas, this relationship states that if the temperature remains constant, the pressure and volume of the gas have an inversely proportional relationship.

• When pressure increases, volume decreases.
• When pressure decreases, volume increases.
• The product of pressure and volume remains constant.

This principle can be expressed through the equation of the ideal gas law: \(PV = nRT\). When temperature (T) is constant, as pressure (P) increases, volume (V) must decrease to maintain the equality.The concept is important because it explains how gases behave under different conditions, such as when compressing a gas in a piston. As pressure applied to the gas increases, the space or volume it occupies reduces and vice-versa. This inverse relationship is visualized in processes where gases are compressed or expanded at constant temperature.

Temperature-Kinetic Energy Relationship

The relationship between temperature and kinetic energy is straightforward but fundamental. In gases, this relationship is often highlighted to explain molecular behavior. The temperature of a gas is a direct measure of the average kinetic energy of its molecules. Therefore: - As temperature increases, the kinetic energy of gas molecules increases. - As temperature decreases, the kinetic energy of gas molecules decreases. Since temperature measures the average motion energy of particles, a higher temperature means more vigorous movements, while a lower temperature indicates slower movements. This principle is crucial when considering any changes that involve heating or cooling gases. For instance, increasing the temperature of a gas will result in faster moving molecules, which typically has effects on pressure and volume depending on the constraints of the container. Understanding this relationship is key to predicting how gases will respond to thermal changes in a variety of scientific and real-world situations.