In a gas where the volume is doubled from its initial volume at 100 K to 400 K, what is the final pressure in relation to its initial pressure Pi?

To understand the relationship between pressure, volume, and temperature in a gas, we can apply the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the absolute temperature in Kelvin.

In this situation, the volume of the gas is doubled while the temperature changes from 100 K to 400 K. To find the final pressure in relation to the initial pressure, we can analyze the change using the formula derived from the ideal gas law.

Initially, let’s denote the initial conditions:

• Initial pressure: Pi

• Initial volume: Vi

• Initial temperature: Ti = 100 K

Final conditions after doubling the volume and raising the temperature:

• Final pressure: Pf

• Final volume: Vf = 2 * Vi

• Final temperature: Tf = 400 K

Using the ideal gas law for both states, we can write:

(1) Initial: ( P_i V_i = nR T_i )

(2) Final: ( P_f V_f = nR T_f )

Substituting the final volume into the second equation gives us:

( P_f (2V_i