When a quantity of monatomic ideal gas expands at a constant pressure of 4.00*104pa, the volume of the gas increases from 2.00*10-3m3 to 8.00*10-3m3?

This can be verified if we know the values of the initial (T1) and final (T2) temperatures. We use the ideal gas equation for this: PV=RT.

P1V1=RT1

(40000 Pa) * (0.002 m^3) = (8.314 m3Pa/molK) (T1)

T1 = 9.62 K

P2V2=RT2

(40000 Pa) * (0.008 m^3) = (8.314 m3Pa/molK) (T2)

T2 = 33.5 K

Thus, this is true if the monoatomic ideal gas is heated from 9.62 K to 33.5 K at constant pressure.

Yes that is correct. We know this because 4.00 x 10 4 Pa is constant. If you have 2.00*10-3m3 then you do the following: (2.00*10^-3) (4.00*10^ 4) = 8.00*10^-3. That is how you get your answer