When an ideal gas expands, its pressure changes according to the law p = aV, where a = const. how many times does the gas

When an ideal gas expands, its pressure changes according to the law p = aV, where a = const. how many times does the gas volume change with an increase in temperature from 200K to 800K

Data: the law of pressure change: P = a * V; a = const; T1 = 200 K; T2 = 800 K.

1) Initial state (Mendeleev-Clapeyron’s law): P1 * V1 = m / M * R * T1; a * V1 * V1 = m / M * R * T1 and a * V12 / T1 = m / M * R = const.

2) Final state: P2 * V2 = m / M * R * T2; a * V2 * V2 = m / M * R * T2 and a * V2 ^ 2 / T2 = m / M * R.

3) From the first two points: a * V2 ^ 2 / T2 = a * V1 ^ 2 / T1, whence V2 ^ 2 / V1 ^ 2 = T2 / T1 and V2 / V1 = √ (T2 / T1) = √ (800 / 200) = 2 times.

Answer: The volume has doubled.