An ideal gas confined in a cylinder by a movable piston at 25°C and 150 KPa is heated at constant pressure to 38°C. The Cp of the gas is (7/2)R. Calculate: AH, AU, Q and W in J/mol
To calculate AH (change in enthalpy), AU (change in internal energy), Q (heat absorbed or released), and W (work done) for this process, we need to use the first law of thermodynamics:
ΔU = Q - W
Where:
ΔU = change in internal energy
Q = heat absorbed or released
W = work done
To calculate AH, we can use the equation:
ΔH = ΔU + PΔV
Where:
ΔH = change in enthalpy
P = pressure
ΔV = change in volume
First, let's calculate the change in volume (ΔV) using the ideal gas law:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in m^3)
n = number of moles
R = ideal gas constant (8.314 J/mol·K)
T = temperature (in Kelvin)
Initial conditions:
P1 = 150 KPa = 150,000 Pa
T1 = 25°C = 298 K
Final conditions:
P2 = 150 KPa = 150,000 Pa
T2 = 38°C = 311 K
Let's begin the calculations:
Step 1: Calculate the change in volume (ΔV)
Using the ideal gas law, solve for V1 and V2:
V1 = (nRT1) / P1
V2 = (nRT2) / P2
ΔV = V2 - V1
Step 2: Calculate ΔH (change in enthalpy)
ΔH = ΔU + PΔV
ΔH = CpΔT
Where:
Cp = specific heat capacity at constant pressure (given as (7/2)R)
ΔT = change in temperature (T2 - T1)
Step 3: Calculate ΔU (change in internal energy)
ΔU = ΔH - PΔV
Step 4: Calculate Q (heat absorbed or released)
Q = ΔU + W
Step 5: Calculate W (work done)
W = -PΔV
Let's perform the calculations:
Step 1: Calculate the change in volume (ΔV)
V1 = (nRT1) / P1
V1 = (n * 8.314 J/mol·K * 298 K) / 150,000 Pa
V2 = (nRT2) / P2
V2 = (n * 8.314 J/mol·K * 311 K) / 150,000 Pa
ΔV = V2 - V1
Step 2: Calculate ΔH (change in enthalpy)
ΔH = CpΔT
ΔH = (7/2)R * (T2 - T1)
Step 3: Calculate ΔU (change in internal energy)
ΔU = ΔH - PΔV
Step 4: Calculate Q (heat absorbed or released)
Q = ΔU + W
Step 5: Calculate W (work done)
W = -PΔV
Substitute the calculated values into the equations to find the final results.