Question

If the absolute temperature of a given quantity of gas is doubled and the pressure tripled, what happens to the volume of the gas?

Answer 1

Answer:

Volume of gas is two-thirds the quotient of pressure and temperature

=$\frac{2P}{3T}$

Explanation:

Ideal gas equation states that:

PV=nRT,

where P = pressure

R = Ideal gas constant

T = temperature

and V = Volume

This equation means that at equal conditions, the volume of a given mass of gas is inversely proportional to its pressure at constant temperature, and directly proportional to the temperature at constant pressure.

Given: P/V = k;     and VT = j (where j and k are constants)

tripled pressure ≡ V = P/3k  and and doubled temp = 2j/T

Assuming constants j=k= unit (1)

V = P/3 = 2/T

=2P/3T.

Answer 2

The gas is considered ideal in nature. The volume of the gas can be  2/3 times the initial volume.

What is an ideal gas equation?

The ideal gas equation gives the relationship for the pressure, volume, and temperature of the gas. It can be given as:

$\rm Pressure\;\times\;Volume=moles\;\times\;constant\;\times\;temperature$

The moles and gas constant are the same for the reaction:

$\rm moles\;\times\;gas\;constant=\dfrac{PV}{T}$

The relationship between the change in the pressure and temperature is given as:

$\rm \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

Substituting the change in the pressure and the temperature:

$\rm \dfrac{PV}{T}=\dfrac{3P\;\times\;V_2}{2T} \\\rm \dfrac{PV\;\times\;2T}{T\;\times\;3P}=V_2\\V _2=\dfrac{2}{3} V$

Thus, the final volume of the gas will be 2/3 times the initial volume.

Learn more about pressure, here:

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