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

Verified step by step guidance

1. 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 pressure, and the change is halving the Kelvin temperature while keeping the pressure constant.
2. 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 ideal gas constant, and T is the temperature in Kelvin.
3. Understand that since the pressure (P) and the number of moles of gas (n) are held constant, and R is a constant, the relationship between volume (V) and temperature (T) can be simplified to V \propto T. This means that the volume is directly proportional to the temperature.
4. Apply the direct proportionality to predict the effect of the temperature change. If the temperature is halved (T becomes T/2), then the volume will also be halved (V becomes V/2) to maintain the equation V \propto T.
5. Conclude that when the Kelvin temperature of the gas is halved while keeping the pressure constant, the volume of the gas in the cylinder will also be halved.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental in understanding how gases behave under various conditions, allowing predictions about changes in volume when temperature or pressure is altered.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin) when pressure is held constant. This means that if the temperature decreases, the volume will also decrease, which is crucial for analyzing the scenario of halving the temperature.

Absolute Temperature

Absolute temperature is measured in Kelvin and is essential for gas law calculations. It starts at absolute zero, where molecular motion ceases. Understanding that temperature must be in Kelvin is vital when applying gas laws, as using Celsius or Fahrenheit would yield incorrect results.