Question

The pressure exerted on a sample of a fixed amount of gas is doubled at constant temperature, and then the temperature of the gas in kelvins is doubled at constant pressure.

What is the final volume of the gas?

What is the final volume of the gas?

The final volume is twice the initial volume.
The final volume of the gas is one-fourth the initial volume.
The final volume of the gas is the same as the initial volume.
The final volume of the gas is four times the initial volume.
The final volume of the gas is one-half the initial volume.

Answer 1

After doubling the pressure of a gas at constant temperature, halving the volume, and then doubling the temperature at constant pressure, which doubles the volume back, the final volume of the gas is the same as the initial volume.

Step-by-step explanation:

To determine the final volume of the gas, we must consider both steps the gas undergoes. In the first step, the pressure of the gas is doubled at constant temperature, which according to Boyle's Law, means the volume is halved since pressure and volume are inversely proportional (P1V1 = P2V2). In the second step, the temperature is doubled (while keeping pressure constant), which according to Charles's Law, means the volume is doubled as well (V1/T1 = V2/T2). When we combine these two changes, the final volume remains the same as the initial volume. This is because the halving of the volume due to the pressure increase is exactly offset by the doubling of the volume due to the temperature increase.

Answer 2

Answer: Option (c) is the correct answer.

Step-by-step explanation:

Boyle's Law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

`P\propto (1)/(V)` (at constant temperature and number of moles)

Charles' Law states that volume is directly proportional to the temperature of the gas at constant pressure and number of moles.

`V\propto T` (at constant pressure and number of moles)

So, when pressure is doubled then volume becomes one-half. But when temperature is doubled then volume will become the same as it was initially.

Thus, we can conclude that the final volume of the gas is the same as the initial volume.