The pressure of a given mass of gas changes from 300Nm^-2 to 120Nm^-2 while the temperature drops from 127°c to -73°c.

The ratio of the final volume to the initial volume is?

since PV = kT, PV/T = k remains constant. So,

300V1/(127+273) = 120V2/(-73+273)
Now just solve for V1/V2

To find the ratio of the final volume to the initial volume, we need to use the combined gas law. The combined gas law relates the pressure, volume, and temperature of a gas.

The formula for the combined gas law is: P1V1/T1 = P2V2/T2

Given:
P1 = 300 Nm^-2 (initial pressure)
P2 = 120 Nm^-2 (final pressure)
T1 = 127°C + 273 = 400 K (initial temperature in Kelvin)
T2 = -73°C + 273 = 200 K (final temperature in Kelvin)

The initial volume and final volume are denoted as V1 and V2 respectively.

We can now substitute the given values into the combined gas law equation:
(300 Nm^-2)(V1)/(400 K) = (120 Nm^-2)(V2)/(200 K)

To find the ratio of the final volume to the initial volume, we can rearrange the equation:
(V2/V1) = [(120 Nm^-2)/(200 K)]/[(300 Nm^-2)/(400 K)]
(V2/V1) = [(120 Nm^-2)(400 K)]/[(200 K)(300 Nm^-2)]
(V2/V1) = 1600 Nm^-2K/600 Nm^-2K

Simplifying the equation:
(V2/V1) = 8/3

Therefore, the ratio of the final volume to the initial volume is 8:3 or 8/3.