A sample of 2.00 mol O2 (assumed perfect) is originally confined in a 20.0L at 273K and 2.24 atm. it undergoes reversable adiabatic expansion until the volume has increased by a factor of 3. Calculate q, w, delta u, delta h, and delta t. Cv=7/2R and cp=5/2R
To calculate q, w, ΔU (change in internal energy), ΔH (change in enthalpy), and ΔT (change in temperature) for the reversible adiabatic expansion of the 2.00 mol O2 sample, we can use the following thermodynamic formulas:
1. First, let's calculate the initial and final conditions:
Initial Volume (V₁) = 20.0 L
Final Volume (V₂) = 20.0 L × 3 = 60.0 L
Initial Temperature (T₁) = 273 K
Final Temperature (T₂) = ?
Initial Pressure (P₁) = 2.24 atm
Final Pressure (P₂) = ?
2. Next, we can calculate the final pressure (P₂) using the ideal gas law equation:
P₁V₁ / T₁ = P₂V₂ / T₂
Plugging in the known values:
(2.24 atm) × (20.0 L) / (273 K) = P₂ × (60.0 L) / T₂
Now, we need to solve for P₂:
P₂ = (2.24 atm) × (20.0 L) × T₂ / (60.0 L × 273 K)
3. With the values of P₂ and T₂, we can proceed to calculate q, w, ΔU, ΔH, and ΔT.
(a) To calculate work (w), we can use the equation for reversible adiabatic processes:
w = ΔU = -n * Cv * ΔT
Where:
n = moles of gas = 2.00 mol
Cv = molar heat capacity at constant volume = (7/2) * R
ΔT = T₂ - T₁
(b) To calculate heat transfer (q), we can use the first law of thermodynamics:
q = ΔU + w
(c) ΔH is equal to ΔU since the process is adiabatic (no heat transfer):
ΔH = ΔU
(d) To calculate ΔT, we use:
ΔT = T₂ - T₁
Now we have all the necessary information to calculate q, w, ΔU, ΔH, and ΔT. Plug in the values and solve the equations using the given values for R:
R = 8.314 J/(mol·K)
Note: The value of R is needed to determine the actual numerical values of the calculated quantities.