a gas at temperature 27 C and at a pressure of 20 atm is allowed to expand and its new volume becomes 10 times that the original and the new pressure is equal to the atmospheric pressure.what is the new temperature of the gas?
To find the new temperature of the gas, we can use the combined gas law equation. The combined gas law relates the initial and final states of a gas using the variables of temperature, pressure, and volume.
The combined gas law equation is given by:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Given:
P1 = 20 atm
V1 = initial volume
T1 = 27°C = 27 + 273.15 = 300.15 K
V2 = 10 * V1 (volume becomes 10 times the original)
P2 = atmospheric pressure
We need to solve for T2. We can rearrange the equation to isolate T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Substituting the given values:
T2 = (1 atm * 10 * V1 * 300.15 K) / (20 atm * V1)
Simplifying the equation:
T2 = 15.0075 K
Therefore, the new temperature of the gas is 15.0075 K.
To find the new temperature of the gas, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = Initial pressure of the gas
V1 = Initial volume of the gas
T1 = Initial temperature of the gas
P2 = Final pressure of the gas
V2 = Final volume of the gas
T2 = Final temperature of the gas
Given:
P1 = 20 atm
V1 = Unknown
T1 = 27°C = 27 + 273.15 K (converting from Celsius to Kelvin)
P2 = Atmospheric pressure (considered to be 1 atm)
V2 = 10 times the original volume = 10 * V1
T2 = Unknown
Plugging these values into the combined gas law equation, we get:
(20 * V1) / (27 + 273.15) = (1 * 10 * V1) / T2
Simplifying the equation, we can cancel out V1:
20 / (27 + 273.15) = 10 / T2
Cross-multiplying the equation, we have:
20 * T2 = (27 + 273.15) * 10
Now, let's solve for T2:
T2 = [(27 + 273.15) * 10] / 20
T2 = (300.15 * 10) / 20
T2 = 3001.5 / 20
T2 = 150.075 K
Converting back to Celsius:
T2 = 150.075 - 273.15
T2 ≈ -123.075°C
Therefore, the new temperature of the gas is approximately -123.075°C.