Explanation:
When the absolute temperature of a gas is doubled, the kinetic energy of its molecules also doubles. As a result, the pressure of the gas increases proportionally. However, if the pressure is reduced to half, the volume of the gas will increase because the gas molecules will spread out more.

Formula:
The relationship between pressure, volume, and temperature of a gas is given by the ideal gas law equation:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature.

Steps:

1. Let's assume that the initial pressure of the gas is P1 and the initial temperature is T1.
2. According to the problem, the absolute temperature of the gas is doubled, which means the new temperature is T2 = 2T1.
3. The pressure of the gas is reduced to half, which means the new pressure is P2 = P1/2.
4. Using the ideal gas law equation, we can find the initial volume of the gas:

P1V = nRT1
V = (nRT1)/P1

5. Similarly, we can find the final volume of the gas:

P2V2 = nRT2
V2 = (nRT2)/P2

6. Substituting the values of P2 and T2 in the above equation, we get:

V2 = (nR(2T1))/P1/2
V2 = 2(nRT1)/P1
V2 = 2V

Answer:
Therefore, the final volume of the gas will be twice the initial volume, which means V2 = 2V.

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