Simultaneous doubling of the absolute temperature of a gas and reduction of its pressure to half, will result in __________ in the volume of the gas.

ANS:B - doubling

To determine the change in volume of a gas when its absolute temperature is doubled and its pressure is halved, we can use the combined gas law, which states: 𝑃1⋅𝑉1𝑇1=𝑃2⋅𝑉2𝑇2T1​P1​⋅V1​​=T2​P2​⋅V2​​ Where:

• 𝑃1P1​ and 𝑇1T1​ are the initial pressure and temperature of the gas,
• 𝑉1V1​ is the initial volume of the gas,
• 𝑃2P2​ and 𝑇2T2​ are the final pressure and temperature of the gas, and
• 𝑉2V2​ is the final volume of the gas.

Given that the absolute temperature (𝑇T) is doubled (which means 𝑇2=2𝑇1T2​=2T1​) and the pressure (𝑃P) is halved (which means 𝑃2=12𝑃1P2​=21​P1​), we can rearrange the combined gas law to solve for 𝑉2V2​: 𝑉2=𝑃1⋅𝑉1⋅𝑇2𝑃2⋅𝑇1V2​=P2​⋅T1​P1​⋅V1​⋅T2​​ 𝑉2=𝑃1⋅𝑉1⋅2𝑇112𝑃1⋅𝑇1V2​=21​P1​⋅T1​P1​⋅V1​⋅2T1​​ 𝑉2=2𝑃1⋅𝑉1⋅𝑇112𝑃1⋅𝑇1V2​=21​P1​⋅T1​2P1​⋅V1​⋅T1​​ 𝑉2=2⋅𝑉112V2​=21​2⋅V1​​ 𝑉2=4𝑉1V2​=4V1​ So, the volume of the gas will increase fourfold. Therefore, the correct answer is "fourfold increase."