A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, a. Has the mass density of the gas changed? If so, by what factor? If not, why not?

Verified step by step guidance

1. Identify the relationship between volume and mass density. Recall that mass density (\( \rho \)) is defined as mass per unit volume (\( \rho = \frac{m}{V} \)).
2. Understand that the mass (m) of the gas remains constant because the system is closed and no gas escapes or is added during the compression.
3. Recognize that the volume (V) of the gas is reduced to half its original volume due to the compression by the piston.
4. Apply the relationship between the initial and final densities. Since the initial volume (\( V_i \)) is halved (\( V_f = \frac{1}{2}V_i \)), and the mass remains constant, the new density (\( \rho_f \)) can be calculated using the formula \( \rho_f = \frac{m}{V_f} = \frac{m}{\frac{1}{2}V_i} = 2 \frac{m}{V_i} = 2 \rho_i \).
5. Conclude that the mass density of the gas has doubled (increased by a factor of 2) as a result of the compression.

Key Concepts

Mass Density

Mass density is defined as the mass of a substance per unit volume, typically expressed in kilograms per cubic meter (kg/m³). It is a crucial property that indicates how much mass is contained in a given volume of material. In the context of gases, density can change with variations in pressure and temperature, but for an ideal gas, it is directly proportional to the number of moles and inversely proportional to volume.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law helps in understanding how changes in volume and pressure affect the behavior of gases, particularly during processes like compression.

Compression of Gases

Compression of gases involves reducing the volume of a gas, which typically increases its pressure and can affect its temperature. According to Boyle's Law, for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. When the volume is halved, the density of the gas increases, as density is mass divided by volume, leading to a higher mass density if the mass remains constant.