Question

HELP PLS

Ideal gas pressure increases 10 times,but absolute temperature decreases 14 times.How much times does the volume of gas changes if its mass does not change?

Answer 1

The volume of the gas decreases 140 times.

Step-by-step explanation:

The equation of state of the ideal gas is described below:

`P\cdot V = n\cdot R_(u)\cdot T` (1)

Where:

`P` - Pressure.

`V` - Volume.

`n` - Molar quantity.

`R_(u)` - Ideal gas constant.

`T` - Temperature.

From this formula we construct the following relationship:

`(P_(1)\cdot V_(1))/(T_(1)) = (P_(2)\cdot V_(2))/(T_(2))` (2)

Where:

`P_(1)`,
`P_(2)` - Initial and final pressure.

`V_(1)`,
`V_(2)` - Initial and final volume.

`T_(1)`,
`T_(2)` - Initial and final temperature.

`(V_(2))/(V_(1)) = ((T_(2))/(T_(1)) )/((P_(2))/(P_(1)) )`

If we know that
`(T_(2))/(T_(1)) = (1)/(14)` and
`(P_(2))/(P_(1)) = 10`, then the change in the volume of the gas is:

`(V_(2))/(V_(1)) = ((1)/(14) )/(10)`

`(V_(2))/(V_(1)) = (1)/(140)`

The volume of the gas decreases 140 times.