AP Physics 2 Exam Question:

A thermodynamic process follows the path ABC shown in the P-V diagram below.

During the process AB, the system undergoes an isothermal expansion at a temperature T1. The volume changes from V1 to V2, and the pressure changes from P1 to P2. The heat added to the system during this process is Q1. During the process BC, the system undergoes an adiabatic compression. The pressure changes from P2 to P3, and the volume changes from V2 to V3. The heat transferred during this process is Q2. During the process CA, the system undergoes an isochoric (constant volume) heating at a temperature T2. The pressure changes from P3 to P4, and the volume remains constant at V3. The heat added to the system during this process is Q3.

a) Determine the work done during the process AB. b) Calculate the change in internal energy of the system during the process AB. c) Determine the work done during the process BC. d) Calculate the change in internal energy of the system during the process BC. e) Determine the work done during the process CA. f) Calculate the change in internal energy of the system during the process CA. g) Calculate the net work done on the system during the entire process ABC.

Answer:

a) To determine the work done during the process AB, we can use the equation:

W = ∫ P dV

Since the process AB is isothermal, the equation for pressure is given by:

PV = constant

Rearranging the equation, we can express pressure in terms of volume:

P = constant / V

Substituting this expression for pressure into the work equation, we get:

W = ∫ (constant / V) dV

Integrating this expression yields:

W = constant * ln(V2/V1)

Therefore, the work done during the process AB is given by:

W_AB = constant * ln(V2/V1)

b) The change in internal energy (ΔU) can be determined using the First Law of Thermodynamics:

ΔU = Q - W

Since process AB is isothermal, the change in internal energy is zero (ΔU_AB = 0) since the temperature remains constant. Therefore, there is no change in internal energy during the process AB.

c) To determine the work done during the process BC, we can use the equation:

W = ∫ P dV

Since the process BC is adiabatic, the equation for pressure is given by:

P * V^γ = constant

Where γ is the adiabatic exponent (ratio of specific heats). Rearranging the equation, we can express pressure in terms of volume:

P = constant / V^γ

Substituting this expression for pressure into the work equation, we get:

W = ∫ (constant / V^γ) dV

Integrating this expression yields:

W = (constant / (1 - γ)) * (V3^(1 - γ) - V2^(1 - γ))

Therefore, the work done during the process BC is given by:

W_BC = (constant / (1 - γ)) * (V3^(1 - γ) - V2^(1 - γ))

d) The change in internal energy (ΔU) can be determined using the First Law of Thermodynamics:

ΔU = Q - W

Since process BC is adiabatic, Q = 0 (no heat transferred). Therefore, the change in internal energy during the process BC is:

ΔU_BC = -W_BC

e) To determine the work done during the process CA, we can use the equation:

W = ∫ P dV

Since the process CA is isochoric (constant volume), the equation for pressure is given by:

P = constant

Therefore, the work done during the process CA is zero (W_CA = 0) since the volume remains constant.

f) The change in internal energy (ΔU) can be determined using the First Law of Thermodynamics:

ΔU = Q - W

Since process CA is isochoric, no work is done (W = 0). Therefore, the change in internal energy during the process CA is:

ΔU_CA = Q3

g) The net work done on the system during the entire process ABC can be determined by summing the work done during each individual process:

Net work = W_AB + W_BC + W_CA

Net work = constant * ln(V2/V1) + (constant / (1 - γ)) * (V3^(1 - γ) - V2^(1 - γ))

That is the net work done on the system during the entire process ABC.

Note:

The constant values, specific values of V1, V2, V3, P1, P2, P3, T1, and T2, as well as the value of γ (adiabatic exponent), were not provided in the question and hence are not specified in the solution. Depending on the specifics of the problem, these values would need to be given or specified in order to evaluate the numerical values for each part of the question.