A sample of an ideal gas goes through the process shown in the figure below.
From A to B, the process is adiabatic; from B to C, it is isobaric with 100kJ
of energy entering the system by heat. From C to D, the process is
isothermal; from D to A, it is isobaric with 150kJ of energy leaving the �system by heat. Determine the difference in internal energy E int,B &
E int,A�
To solve this problem, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W).
Mathematically, this can be expressed as:
ΔU = Q - W
Since the process from A to B is adiabatic, no heat is exchanged during this process, so Q_ab = 0. The work done during the adiabatic process can be written as:
W_ab = -ΔU_ab
Since the process from B to C is isobaric, the heat added to the system is 100 kJ, so Q_bc = 100 kJ. The work done by the system during the isobaric process is equal to the pressure multiplied by the change in volume:
W_bc = P(V_C - V_B)
Since the process from C to D is isothermal, the heat added to the system is equal to the work done by the system:
Q_cd = -W_cd
Since the process from D to A is isobaric, the heat added is -150 kJ:
Q_da = -150 kJ
Now, we can calculate the net change in internal energy by summing up the internal energy changes for each process:
ΔU = ΔU_ab + ΔU_bc + ΔU_cd + ΔU_da
ΔU_ab = -W_ab
ΔU_bc = Q_bc - W_bc
ΔU_cd = 0
ΔU_da = Q_da - (-W_da) = -150 kJ
Now we substitute the values and calculate E_int,B & E_int,A.
system by heat. Determine the difference in internal energy Eint,B &
Eint,A�
To determine the difference in internal energy (ΔEint) between points B and A, we need to calculate the change in internal energy for each process and then find the total change.
1. Adiabatic Process (A to B):
Since the process is adiabatic, there is no heat exchange, so Q_ab = 0.
The work done in an adiabatic process is given by W_ab = -ΔU_ab.
Therefore, ΔU_ab = -W_ab
2. Isobaric Process (B to C):
During the isobaric process, the heat added is 100 kJ, so Q_bc = 100 kJ.
The work done in an isobaric process is W_bc = P(V_C - V_B).
For an isobaric process, ΔU = Q - W. Thus, ΔU_bc = Q_bc - W_bc.
3. Isothermal Process (C to D):
Since the process is isothermal, the heat added is equal to the work done, so Q_cd = -W_cd.
Therefore, ΔU_cd = 0.
4. Isobaric Process (D to A):
During the isobaric process, the heat added is -150 kJ, so Q_da = -150 kJ.
The work done in an isobaric process is given by W_da = P(V_A - V_D), and ΔU_da = Q_da - W_da.
We can now calculate the change in internal energy for each process using the given information and then add up all the changes to get the total change in internal energy between points B and A.