a sample of helium gas is in a closed system with a movable piston. the volume of the gas sample is changed when both the temperature and the pressure of the sample are increased. the table below shows the initial temperature, pressure, and volume of the gas sample, as well as the final temperature and pressure of the sample. what is the final volume of the sample?

To determine the final volume of the sample, we need more information. Could you please provide the values in the table, including the initial temperature, pressure, and volume of the gas sample, as well as the final temperature and pressure of the sample?

To determine the final volume of the helium gas sample, we need to use the gas laws: Boyle's law and Charles's law.

Boyle's law states that at a constant temperature, the product of the pressure and volume of a gas remains constant. It can be mathematically expressed as: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Charles's law states that at constant pressure, the volume of a gas is directly proportional to its temperature. It can be expressed as: V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.

Using both of these laws, we can calculate the final volume of the helium gas sample by rearranging the equations and plugging in the given values.

Let's denote the initial temperature, pressure, and volume as follows:
Initial temperature (T1) = ?
Initial pressure (P1) = ?
Initial volume (V1) = ?
Final temperature (T2) = Given
Final pressure (P2) = Given
Final volume (V2) = ?

Since the table does not provide specific initial values for temperature, pressure, and volume, we need those values to solve for the final volume.

Please provide the specific initial values for temperature, pressure, and volume of the gas sample, or confirm if they are given in the question or table.

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(2)(500)(300)/(500)(7)