Final answer:
Charles's Law describes the direct proportionality between the volume of a gas and its temperature at constant pressure, while Boyle's Law describes the inverse proportionality between the pressure and the volume of a gas at constant temperature. A piston in a cylinder will move outward as the temperature increases (Charles's Law) or inward as the pressure increases (Boyle's Law), visually demonstrating these principles.
Step-by-step explanation:
The piston in a container is intimately related to the concepts of Charles's and Boyle's laws, which are fundamental principles in thermodynamics and gas laws. Charles's Law describes the direct proportionality between the volume (V) of a gas and its absolute temperature (T) when pressure is held constant, which can be represented by the equation V ∓ T. This implies that if the temperature of a gas is doubled, the volume will also double, assuming that the pressure and the amount of gas remain constant. This can be visualized by heating a piston in a cylinder: as the gas heats up, the molecules move faster, increasing the kinetic energy and pushing the piston outwards, doubling the volume of the gas.
On the other hand, Boyle's Law states that the pressure (P) of a gas is inversely proportional to its volume (V) at a constant temperature, illustrated as P ∓ 1/V. This means that if the pressure is doubled, the volume of the gas is reduced by half, assuming the temperature and the amount of gas stay the same. In practical terms, if we press down on a piston, increasing the pressure inside the cylinder, the volume of the contained gas will decrease correspondingly.
Graphically, both laws can be represented with plots: a V versus T graph for Charles's Law showing a straight line emanating from the origin, and a P versus V graph for Boyle's Law showing a hyperbolic curve. In both cases, the shape of the graph is determined by the mathematical relationship of the variable: linear for Charles's Law and hyperbolic for Boyle's Law.