Respuesta :
Answer:
the volume of the gas becomes 1/4 the original volume
Explanation:
The ideal gas law gives the following relationship between temperature, pressure, and volume:
[tex]PV=n\cdot r\cdot T[/tex]where
P = pressure
V = volume
n = number of moles
r = gas constant
T = temperature
Now let us call the initial pressure, volume, and temperature P0, V0, and T0 respectively; then we have
[tex]P_0V_0=\text{nrT}_0[/tex]Solving for V0 gives
[tex]\boxed{V_0=\frac{\text{nrT}_0}{P_0}}[/tex]Now, what happens if the new pressure is 2 times the initial pressure ( P = 2 P0) and the new temperature is reduced to half ( T = 1/2 T0).
We find out by putting in P = 2 P0 and T = 1/2 T0 into the above equation to get:
[tex]V=\frac{nr(\frac{1}{2}T_0)_{}}{2P_0}[/tex]which simplifies to give us
[tex]V=\frac{nrT_0_{}}{4P_0}=\frac{1}{4}(\frac{nrT_0}{P_0})[/tex]Realising that
[tex]V_0=\frac{\text{nrT}_0}{P_0}[/tex]the above becomes
[tex]V=\frac{1}{4}(\frac{nrT_0}{P_0})=\frac{1}{4}V_0[/tex]Hence, our final result is
[tex]\boxed{V=\frac{1}{4}V_0}[/tex]meaning that the new volume is one-fourth of the original volume.
