the volume v of a gas varies directly as temperature t and inversely as pressure p. if the volume of gas is 800 ml at a temperature at 25 degrees celsius with the pressure of 40,000 Pa. what is the volume of the same gas at a temperature of 28 degrees celsius and the pressure of 80,000 Pa?​

Sagot :

Given:

[tex]P_{1} = \text{40,000 Pa}[/tex]

[tex]T_{1} = \text{25°C + 273 = 298 K}[/tex]

[tex]V_{1} = \text{800 mL}[/tex]

[tex]P_{2} = \text{80,000 Pa}[/tex]

[tex]T_{2} = \text{28°C + 273 = 301 K}[/tex]

Unknown:

[tex]V_{2}[/tex]

Solution:

[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}[/tex]

[tex]V_{2} = V_{1} × \frac{P_{1}}{P_{2}} × \frac{T_{2}}{T_{1}}[/tex]

[tex]V_{2} = \text{800 mL} × \frac{\text{40,000 Pa}}{\text{80,000 Pa}} × \frac{\text{301 K}}{\text{298 K}}[/tex]

[tex]\boxed{V_{2} = \text{404 mL}}[/tex]

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