1) 0.19 litre of an ideal monatomic gas (Cv,m = 3R/2) initially at 83 °C and 47 atm pressure undergo an expansion against a constant external pressure of 1.19 atm, and do 2.3 kJ of work. The final pressure of the gas is 1.19 atm. Calculate the change in enthalpy, ΔH
2) Calculate the work, w, (in J) when 5.2 litre of an ideal gas at an initial pressure of 45.1 atm is expanded isothermally to a final pressure of 1.56 atm against a constant exteral pressure of 1.56 atm.
-I used the equation: w = -Pext(ΔV) and got -821.94 in J..it's wrong
Thank you!! :)
Try this for 2. It would have helped if you showed you work so we wouldn't need to guess what you did.
p1v1 = p2v2.
45.1*5.2 = 1.56*v2
I obtained approx 150 L for v2 but you should get a better answer.
Then work = -1.56(V2-V1) which gives an answer in L*atm. That x 101.325 will convert to J. My answer is approx -22 kJ.
1) dH = 3511.63 J
2) w = -22940.26 J
To solve these problems, we can use the first law of thermodynamics, which states that the change in internal energy (U) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
ΔU = Q - W
1) For the first problem, we are given the initial and final pressure, as well as the volume at the initial pressure. Since the process is an expansion against a constant external pressure, the work done can be calculated using the formula:
W = -Pext * ΔV
Where Pext is the external pressure and ΔV is the change in volume.
To find the change in volume, we can use the ideal gas law:
P1 * V1 / T1 = P2 * V2 / T2
Where P1 and T1 are the initial pressure and temperature, V1 is the initial volume, and P2 and T2 are the final pressure and temperature.
We can rearrange this equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Now that we have the change in volume, we can substitute it into the work formula:
W = -Pext * ΔV = -Pext * (V2 - V1)
Since the work done is given as 2.3 kJ, we need to convert it to Joules by multiplying by 1000:
W = 2.3 kJ * 1000 = 2300 J
Now we can substitute the given values into the equation:
W = -Pext * (V2 - V1) = -1.19 atm * [(P1 * V1 * T2) / (P2 * T1) - V1]
We know the value for V1 is 0.19 liters, but the temperatures are given in Celsius. We need to convert them to Kelvin before substituting into the equation:
T1 = 83 °C + 273.15 = 356.15 K
T2 = 47 °C + 273.15 = 320.15 K
Substituting all the values into the equation, we can solve for P1:
2300 J = -1.19 atm * [(P1 * 0.19 L * 320.15 K) / (1.19 atm * 356.15 K) - 0.19 L]
Simplifying the equation will give us the value of P1.
Once we have the value of P1, we can calculate the change in enthalpy (ΔH) using the equation:
ΔH = ΔU + PΔV
Where ΔU is the change in internal energy, which can be calculated using the equation:
ΔU = Q - W
Since we know the work done (W), we can solve for ΔU. Then we can substitute the values into the equation to find ΔH.