To determine the net heat added to the gas during the process CA, we can utilize the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This can be expressed mathematically as:

First Law of Thermodynamics

The equation can be written as:

ΔU = Q - W

Where:

• ΔU is the change in internal energy.
• Q is the heat added to the system.
• W is the work done by the system.

Analyzing the Given Information

From the problem, we have the following values:

• Q_AB = 20 J (heat added during process AB)
• Q_BC = 0 J (no heat added during process BC)
• W_BCA = -15 J (work done on the gas during the process from B to C to A)

Calculating the Net Heat Added in Process CA

To find the net heat added during the process CA, we need to consider the heat added during the entire cycle and the work done. The total heat added to the gas during the entire cycle can be calculated as:

Q_net = Q_AB + Q_BC + Q_CA

Since we know Q_AB and Q_BC, we can express Q_CA in terms of the work done:

ΔU_CA = Q_CA - W_BCA

Since the process is cyclic, the change in internal energy over one complete cycle is zero:

ΔU_cycle = 0 = Q_AB + Q_BC + Q_CA - W_BCA

Substituting the Known Values

Now we can substitute the known values into the equation:

0 = 20 J + 0 J + Q_CA - (-15 J)

This simplifies to:

0 = 20 J + Q_CA + 15 J

Combining the terms gives:

0 = 35 J + Q_CA

Solving for Q_CA

To isolate Q_CA, we can rearrange the equation:

Q_CA = -35 J

Final Result

This indicates that during the process CA, the gas actually loses heat, amounting to 35 J. In summary, the net heat added to the gas during the process CA is -35 J, meaning that heat is being removed from the gas rather than added.