The pressure, volume, and temperature of an ideal gas are given respectively as P1, V1, T1. what is the volume V2 of the gas if its pressure is reduced by half and the temperature is tripled?
P1 V1/T1 = P2V2/T2 = n R
P2 = .5 P1
T2 = 3 T1
P1 V1/T1 = .5P1 V2/3T1
V1 = V2 (.5/3) = V2/6
so
V2 = 6 V1
To find the new volume V2 of the gas when its pressure is reduced by half and the temperature is tripled, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
In this case, we are given the initial conditions as P1, V1, and T1. Let's assume that the number of moles (n) and the gas constant (R) remain constant. Now, we can write the initial gas equation as:
P1 * V1 = n * R * T1
To find the new volume V2, we need to find the new pressure P2 and temperature T2 first.
1. Pressure (P2) is reduced by half:
P2 = P1 / 2
2. Temperature (T2) is tripled:
T2 = 3 * T1
Now we can substitute the new pressure (P2) and temperature (T2) into the ideal gas equation:
P2 * V2 = n * R * T2
Substituting the values we found:
(P1 / 2) * V2 = n * R * (3 * T1)
We can cancel n and R on both sides:
(P1 / 2) * V2 = 3 * P1 * V1
Finally, we can solve for V2:
V2 = 3 * P1 * V1 / (P1 / 2)
Simplifying further:
V2 = (3 * P1 * V1) * (2 / P1)
V2 = 6 * V1
Therefore, the new volume V2 of the gas is 6 times the initial volume V1 when its pressure is reduced by half and the temperature is tripled.
To find the volume of the gas (V2) when the pressure is reduced by half and the temperature is tripled, you can use the combined gas law. The combined gas law states that for a given amount of gas, the pressure, volume, and temperature are related by the equation:
(P1 × V1) / T1 = (P2 × V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (to be determined)
T2 = final temperature
In this case, the initial pressure (P1) and volume (V1) are given as P1 and V1 respectively, while the initial temperature (T1) is also given as T1. The final pressure (P2) is half of the initial pressure (P1/2), since it's reduced by half. The final temperature (T2) is tripled, so it is 3 times the initial temperature (3 × T1).
Now, we can plug these values into the combined gas law equation:
(P1 × V1) / T1 = (P2 × V2) / T2
(P1 × V1) / T1 = ((P1/2) × V2) / (3 × T1)
Simplifying further:
2 × (P1 × V1) = P1 × V2 / (3 × T1)
Now, let's rearrange the equation to solve for V2:
V2 = (2 × P1 × V1 × 3 × T1) / P1
Canceling out the P1 term:
V2 = (2 × V1 × 3 × T1) / 1
Simplifying further:
V2 = 6 × V1 × T1
Therefore, the volume (V2) of the gas when its pressure is reduced by half and the temperature is tripled is equal to 6 times the initial volume (V1) multiplied by the initial temperature (T1).