The figure below shows two paths that may be taken by a gas to go from a state A to state C.In process AB, 400J of heat is added to the system and in process BC, 100J of heat is added to the system. The heat absorbed by the system in the process AC will be:




A. 460 JB. 300 JC. 380 JD. 500 J

To find the total heat absorbed by the system in the process AC, you can use the first law of thermodynamics, which states:

ΔU = Q - W

Where:
ΔU = change in internal energy
Q = heat added to the system
W = work done by the system

In this case, you are interested in the heat added to the system (Q) during the process AC. Since the process is a combination of AB and BC, you can calculate the change in internal energy for each of these processes and then add them together to find the total change in internal energy for AC. Once you have the total change in internal energy, you can find the heat added to the system during AC.

Let's calculate it step by step:

For process AB, 400 J of heat is added to the system, and no work is done (assuming no change in volume is specified). Therefore, for AB:
ΔU_AB = Q_AB - W_AB
ΔU_AB = 400 J - 0 J
ΔU_AB = 400 J

For process BC, 100 J of heat is added to the system, and no work is done (again, assuming no change in volume). Therefore, for BC:
ΔU_BC = Q_BC - W_BC
ΔU_BC = 100 J - 0 J
ΔU_BC = 100 J

Now, to find the total change in internal energy for process AC, you simply add the changes in internal energy for AB and BC:

ΔU_AC = ΔU_AB + ΔU_BC
ΔU_AC = 400 J + 100 J
ΔU_AC = 500 J

Now, you can find the heat added to the system during process AC using the first law of thermodynamics:

ΔU_AC = Q_AC - W_AC
500 J = Q_AC - W_AC

Since no work is done during process AC (W_AC = 0 J), you can simplify the equation:

500 J = Q_AC

So, the heat absorbed by the system in the process AC is 500 J. Therefore, the correct answer is option D: 500 J.