When the temperature of 4 dm cube of an ideal gas is increased from 200k to halved,calculate the final volume of the gas
Use (V1/T1) = (V2/T2)
Post your work if you get stuck.
To calculate the final volume of the gas after the temperature is halved, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature in Kelvin
Since the number of moles (n) and the pressure (P) are not given and we are only interested in the change in volume, we can rearrange the equation as follows:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure
V1 = initial volume (4 dm³)
T1 = initial temperature (200 K)
P2 = final pressure (assumed to be constant)
V2 = final volume (to be determined)
T2 = final temperature (halved)
Given:
P1V1 / T1 = P2V2 / T2
T2 = T1 / 2 (since the initial temperature is halved)
Plugging the values into the equation:
P1 * 4 dm³ / 200 K = P2 * V2 / (200 K / 2)
Simplifying:
P1 * 4 dm³ = 2 * P2 * V2
Now, we need to have values for P1 and P2 in order to calculate V2. If the pressure is constant, then P2 = P1. Assuming this to be the case, we can continue with the equation:
4 dm³ = 2 * P1 * V2
Now, we need to convert the volume from dm³ to m³:
1 dm³ = 0.001 m³
Substituting the values:
4 * 0.001 m³ = 2 * P1 * V2
0.004 m³ = 2 * P1 * V2
Dividing both sides by 2P1:
V2 = 0.004 m³ / (2 * P1)
Therefore, the final volume of the gas after the temperature is halved would be 0.004 m³ divided by twice the initial pressure (P1).
To calculate the final volume of the gas, we can use the ideal gas law, which states that the product of pressure (P) and volume (V) is proportional to the product of the number of moles (n) and the temperature (T) of the gas. Mathematically, it can be written as:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = Ideal gas constant
T = Temperature of the gas
In this case, we have a fixed volume of gas, so the equation can be simplified to:
P1/T1 = P2/T2
Where:
P1 = Initial pressure of the gas
T1 = Initial temperature of the gas
P2 = Final pressure of the gas (unchanged for this problem)
T2 = Final temperature of the gas (which is half of the initial temperature)
Let's assume the initial pressure of the gas to be P1. Since the pressure does not change, the equation becomes:
P1/T1 = P2/(T1/2)
Simplifying further:
2P1 = P2
Now, to find the final volume of the gas, we need to use the given initial volume and the fact that the number of moles and pressure remain constant.
Since the volume is halved when the temperature is halved, the final volume would be halved as well. Therefore, the final volume is:
Final Volume = (Initial Volume) / 2
Given that the initial volume is 4 dm^3, the final volume would be:
Final Volume = 4 dm^3 / 2
Final Volume = 2 dm^3
So, the final volume of the gas would be 2 dm^3.