In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B, an amount of work equal to 22.3 J is done on the system. If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal, how much is the net work done by the system in the latter case? (Take 1 cal = 4.19 J)

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When a gas undergoes an adiabatic process, it means that there is no exchange of heat between the system and its surroundings. Hence, the first scenario, where the adiabatic process results in work done on the system, indicates that the change in internal energy is solely due to work done.

Given that the work done in the adiabatic process from state A to state B is 22.3 J, 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 is adiabatic, Q = 0, so:

ΔU = -W

Therefore, the change in internal energy is equal to the negative of the work done on the system. So, ΔU = -22.3 J.

Now, let's consider the second scenario where the net heat absorbed by the system is 9.35 cal. We need to convert this to joules using the conversion factor provided: 1 cal = 4.19 J.

So, 9.35 cal * 4.19 J/cal = 39.1865 J.

In this scenario, there is a net heat absorbed by the system, indicating that the change in internal energy is due to both heat transfer and work done. Therefore, we need to calculate the net work done by the system.

Using the first law of thermodynamics again:

ΔU = Q - W

ΔU = 39.1865 J (from the heat absorbed)

From the previous scenario, we know that ΔU = -22.3 J.

So,

-22.3 J = 39.1865 J - W

W = 39.1865 J + 22.3 J

W ≈ 61.4865 J

Therefore, the net work done by the system in the latter case, where the net heat absorbed is 9.35 cal, is approximately 61.4865 J.