Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you were to do the following? (a) Triple the Kelvin temperature while holding the volume constant

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Identify the initial conditions and the changes applied to the system. In this case, the initial condition is the gas in the cylinder at a certain temperature and volume, and the change is tripling the Kelvin temperature while keeping the volume constant.

Recall the ideal gas law, which is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

Understand that since the volume (V) and the amount of gas (n) are held constant, and R is a constant, the relationship between pressure (P) and temperature (T) can be simplified to P \(\propto\) T. This means that pressure is directly proportional to temperature when volume and the amount of gas are constant.

Apply the direct proportionality to the change in temperature. Since the temperature is tripled, and the pressure is directly proportional to the temperature, the pressure inside the cylinder will also increase.

Conclude that tripling the Kelvin temperature of the gas while keeping the volume constant will result in a tripling of the pressure inside the cylinder.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and the amount of gas. The most relevant here is the Ideal Gas Law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. Understanding these relationships is crucial for predicting how changes in one variable affect others.

Charles's Law

Charles's Law specifically relates the volume and temperature of a gas at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin). While this question holds volume constant, recognizing the implications of temperature changes on pressure is essential, as it leads to an understanding of how gas behavior changes under different conditions.

Pressure-Temperature Relationship

The pressure-temperature relationship indicates that, at constant volume, increasing the temperature of a gas will increase its pressure. This is due to the increased kinetic energy of gas molecules, which collide more frequently and forcefully with the walls of the container. Thus, tripling the Kelvin temperature while keeping the volume constant will result in a proportional increase in pressure.

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