Answer :
According to ideal gas equation, we know for 1 mole of gas: PV=RT
where P = pressure, T = temperature, R = gas constant, V= volume
If '1' and '2' indicates initial and final experimental conditions, we have
[tex] \frac{P1V1}{P2V2} = \frac{T1}{T2} [/tex]
Given that: V1 = 100.0 kPa, T1 = 100.0 K, V1 = 2.0 m3, T2 = 400 K, P2 = 200.0 kPa
∴ on rearranging above eq., we get V2 = [tex] \frac{P1V1T2}{T1} = \frac{100 X 2 X 400}{200X100} [/tex]
∴ V2 = 4 m3
where P = pressure, T = temperature, R = gas constant, V= volume
If '1' and '2' indicates initial and final experimental conditions, we have
[tex] \frac{P1V1}{P2V2} = \frac{T1}{T2} [/tex]
Given that: V1 = 100.0 kPa, T1 = 100.0 K, V1 = 2.0 m3, T2 = 400 K, P2 = 200.0 kPa
∴ on rearranging above eq., we get V2 = [tex] \frac{P1V1T2}{T1} = \frac{100 X 2 X 400}{200X100} [/tex]
∴ V2 = 4 m3
The ideal equation relates the temperature with the pressure and the volume of the gas. When the temperature is increased then the volume will be 4 cubic meters.
What is an ideal gas equation?
An ideal gas equation depicts the relation between the temperature to that of the volume and the pressure of the gas.
The formula is given as,
[tex]\rm \dfrac{P_{1}V_{1}}{P_{2}V_{2}} = \rm \dfrac{T_{1}}{T_{2}}[/tex]
Given,
Initial pressure = 100 kPa
Initial volume = 2 cubic meter
Initial temperature = 100 K
Final pressure = 200 kPa
Final volume = ?
Final temperature = 400 K
The final volume is calculated as:
[tex]\begin{aligned} \rm V_{2} &= \rm \dfrac{P_{1}V_{1}T_{2}}{T_{1}}\\\\&= \dfrac{100\times 2 \times 400}{200 \times 100}\\\\&= 4 \;\rm m^{3}\end{aligned}[/tex]
Therefore, 4 cubic meters is the volume of the final gas.
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