A certain mass of a gas at 273k temperature and one atmospheric pressure is expanded to 3 times its original volume under adiabatic conditions.Calculate the resulting temperature and pressure( take the value of (gamma)= 1.4).
Under adiabatic conditions (dQ = 0),
P2 / P1 = (V1 / V2)^γ
where
P1 and P2 = initial and final pressures respectively
V1 and V2 = initial and final volumes respectively
γ = heat capacity ratio = Cp/Cv
Substituting,
P2 / 1 = (V1 / 3*V1)^1.4
P2 = 0.2148 atm
Also, under adiabatic conditions,
T2 / T1 = (V1 / V2)^(γ-1)
where
T1 and T2 = initial and final absolute temperatures respectively
Substituting,
T2 / 273 = (V1 / 3*V1)^(1.4-1)
T2 = 175.92 K
hope this helps? `u`
Thanks Mr jai for this suggestion
You're welcome~!
I'm a girl though, but it's alright~ :D
To calculate the resulting temperature and pressure after the gas is expanded under adiabatic conditions, we can use the relationship between temperature, pressure, volume, and the adiabatic index (gamma).
Let's denote the initial temperature as T1, the initial pressure as P1, the initial volume as V1, and the final temperature as T2, the final pressure as P2, and the final volume as V2.
According to the adiabatic process equation, we have:
P1 * V1^gamma = P2 * V2^gamma
Where gamma is the adiabatic index, which is given as 1.4.
We are given that the initial temperature T1 = 273 K and the final volume V2 = 3 * V1.
Now, we can rearrange the equation to solve for the final pressure P2:
P2 = P1 * (V1/V2)^gamma
P2 = P1 * (V1/(3*V1))^gamma
= P1 * (1/3)^gamma
= P1 * (1/3)^1.4
Similarly, we can solve for the final temperature T2 using the ideal gas law equation:
P2 * V2 / T2 = P1 * V1 / T1
Since we know that V2 = 3 * V1, we can substitute this value and rearrange the equation to solve for T2:
T2 = T1 * (P2 * V2) / (P1 * V1)
= T1 * (P1 * (V1/V2)^(gamma-1)) / (P1 * V1)
= T1 * ((1/3)^(gamma-1))
= T1 * ((1/3)^0.4)
Now, plugging in the given values:
T1 = 273 K
gamma = 1.4
P2 = P1 * (1/3)^1.4
T2 = T1 * ((1/3)^0.4)
Calculating these values will give you the resulting temperature (T2) and pressure (P2) of the gas after expansion.