What happens to the pressure of a gas under the following...

What happens to the pressure of a gas under the following conditions?
a. The absolute temperature is halved and the volume doubles.
b. Both the absolute temperature and the volume double.
c. The absolute temperature increases by $75 \%,$ and the volume decreases by $50 \%$.

Key Concepts

Direct and Inverse Proportionality in Gas Behavior

Gas behavior exhibits direct proportionality between pressure and absolute temperature, meaning that as the temperature increases (with constant volume), the pressure increases, and vice versa. Similarly, gas behavior exhibits inverse proportionality between pressure and volume, meaning that if the volume increases (with constant temperature), the pressure decreases. These relationships allow for the prediction of changes in pressure when both temperature and volume are altered concurrently.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental equation in thermodynamics that relates the pressure (P), volume (V), and absolute temperature (T) of a sample of gas with a constant amount of substance (n) and the gas constant (R). It provides a framework for understanding how changes in temperature or volume affect the pressure of an ideal gas.

Combined Gas Law

The Combined Gas Law is a rearrangement of the Ideal Gas Law that is used when the amount of gas is held constant. It directly relates the initial and final states of a gas using the ratio P/T being proportional to 1/V, encapsulating the idea that pressure is directly proportional to temperature and inversely proportional to volume. This law is particularly useful for analyzing scenarios where variables such as temperature and volume change simultaneously.

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