A sample of H2(g) expands adiabatically and reversibly from a state 1 where p1 = 200000Pa,V1 = 0.002m3 and T1 = 300K to a state 2 where V2 = 0.004m3.Assume the gas to behave as an ideal gas calculate the final temperature and its pressure.Use the constant value,Cp = 28.8 j/molK.Calculate n(moles of H2),change in internal energy,w and enthalpy change#### anyone to help me especially n and final temperature
the final temperature is 35
To calculate the final temperature and the pressure of the sample of H2, we need to use the first law of thermodynamics, which states that:
ΔU = Q - W
Where:
ΔU = Change in internal energy
Q = Heat added
W = Work done
Since the expansion is adiabatic, there is no heat transferred (Q = 0). Additionally, since the gas is ideal, we can use the ideal gas law to relate the pressure, volume, and temperature:
PV = nRT
Where:
P = Pressure
V = Volume
n = moles of gas
R = Ideal gas constant
T = Temperature
Given that the expansion is reversible, we can use the adiabatic reversible expansion equation:
P1V1^(γ) = P2V2^(γ)
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
γ = Cp / Cv
Let's calculate the values step by step:
Step 1: Calculate the moles of H2 (n)
We can use the ideal gas equation and the given values to find n:
n = PV / RT
n = (P1 * V1) / (RT1)
Step 2: Calculate the final temperature (T2)
Using the adiabatic reversible expansion equation, we can solve for T2:
T2 = T1 * (V1 / V2)^((γ - 1) / γ)
Step 3: Calculate the final pressure (P2)
We can use the ideal gas equation and the final temperature to find P2:
P2 = (n * R * T2) / V2
Step 4: Calculate the change in internal energy (ΔU)
Since it's an adiabatic process, there is no heat transfer (Q = 0). Therefore:
ΔU = 0 - W
ΔU = -W
Step 5: Calculate the work done (W)
The work done can be calculated using the equation:
W = Cp * n * (T2 - T1)
Step 6: Calculate the enthalpy change (ΔH)
The enthalpy change can be calculated using the equation:
ΔH = ΔU + P2 * (V2 - V1)
With these calculations, you can find the final temperature, final pressure, change in internal energy, work done, and enthalpy change. Plug in the given values and the necessary constant to get the final result.