Gas Laws

The ratio of specific heats for an ideal gas is given by: For a monatomic ideal gas, the value of is , because a monatomic gas has only translational degrees of freedom. For a diatomic ideal gas, the value of is , because a diatomic gas has translational and rotational degrees of freedom. At high temperatures, it may also have vibrational degrees of freedom, but in this case, we're assuming it to be a simple diatomic molecule. Thus, for monatomic and for diatomic.

The ideal gas equation is an approximation that assumes the gas molecules do not interact with each other and that their volume is negligible compared to the volume of the container. This equation is most accurate under conditions of high temperature and low pressure because, under these conditions, the gas molecules are far apart, and intermolecular forces (such as attraction or repulsion) are negligible. At low temperatures and high pressures, real gases deviate from ideal behavior due to intermolecular forces and the finite volume of gas molecules.

Step 1: Use the combined gas law. The combined gas law is derived from the ideal gas law and relates pressure, volume, and temperature: where: - , , and are the initial pressure, volume, and temperature, - , , and are the final pressure, volume, and temperature. Step 2: Substitute the known values. Given: - , - , - , - , - . We need to solve for . Step 3: Solve for . Answer: Therefore, the volume of the gas after the changes is .