In changing the state of a gas adiabatically from an equilibrium state to another equilibrium state , an amount of work equal to 22.3 J is done on the system. If the gas is taken from state to 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)
The net work done by the system in the latter case is 16.88 J (or approximately 16.9 J).
Explanation
This question applies the First Law of Thermodynamics and the concept that internal energy is a state function. In an adiabatic process, Q = 0, so from ΔQ = ΔU + W, we get ΔU = -W. Since work done ON the system is 22.3 J, work done BY the system is -22.3 J, making ΔU = 22.3 J. For any process between the same two states, ΔU remains the same. Using the heat absorbed (converted to Joules) and the First Law, we calculate the work done by the system.
Solution Steps
Step 1: For the adiabatic process from state A to B, heat exchange Q = 0. Given work done ON the system = 22.3 J, so work done BY the system W₁ = -22.3 J.
Step 2: Using First Law of Thermodynamics (ΔQ = ΔU + W) for adiabatic process: 0 = ΔU + (-22.3), therefore ΔU = 22.3 J.
Step 3: Since internal energy is a state function, ΔU remains 22.3 J for any process between states A and B.
Step 4: For the second process, heat absorbed Q₂ = 9.35 cal = = 39.18 J.
Step 5: Applying First Law: Q₂ = ΔU + W₂, so 39.18 = 22.3 + W₂, therefore W₂ = 39.18 - 22.3 = 16.88 J.