# How Is Energy Managed in a Cyclic Process of an Ideal Diatomic Gas?

• pentazoid
In summary, the conversation discusses an ideal diatomic gas undergoing a rectangular cyclic process in a cylinder with a movable piston. The temperature is such that rotational degrees of freedom are active but vibrational modes are frozen out. The only type of work done on the gas is quasistatic compression-expansion work. For each of the four steps A through D, the work done on the gas, heat added to the gas, and change in energy content are calculated using equations such as the ideal gas law and the equipartition theorem for energy. The heat is calculated using the equation delta(U) = Q + W, where Q = delta(U) - W.
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## Homework Statement

An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process. Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are "frozen out". Also Assume that the only type the only type of work done on the gas is quasistatic compression-expansion work.

For each of the four steeps A through D , compute the work on the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in the terms P_1, P_2, V_1, and V_2

Steps A, B, C and D are drawn on a PV diagram

State A: Pressure changes, Volume is constant(V_1 is constant)

State B: Volume changes, Pressure is constat(P_2 is constant)

State C: Pressure changes , Volume is constant)(V_2 is constant)

State D: Volume changes, pressure is constant(P_1 is constant)

## Homework Equations

delta(U)=W+Q

delta(U)=f/2*NkT (equipartition thm. for energy)

NkT=PV (ideal gas law)

W=-integral(from V_initial to V_final) P(V) dV (quasistatic)

W= -P*delta(V) (quasistatic)

## The Attempt at a Solution

W_A=0
W_B=-P_2(V_2-V_1)=
W_C=0
W_A=-P_1(V_1-V_2)=P_1(V_2-V_1)

U=f/2*N*k*delta(T)=f/2*P*delta(V)
since NkT=PV
f=5 since air is a polyatomic molecule

U_A=5/2*(P_2*V_1-P_1*V_1)=5/2*(V_1)*(P_2-P_1)
U_B=5/2*(P_2*V_2-P_2*V_1)=5/2*(P_2)*(V_2-V_1)
U_C=5/2*(P_1*V_2-P_2*V_2)=5/2*(V_2)*(P_1-P_2)
U_D=5/2*(P_1*V_1-P_1*V_2)=5/2*(P_1)*(V_1-V_2)

to calculate the heat, you would use the equation delta(U)=Q+W,Q=delta(U)-W for each of the four states.

Did anyone not understand my question?

## 1. What is an ideal diatomic gas?

An ideal diatomic gas is a hypothetical gas composed of two atoms that have no interaction with each other and follow the laws of ideal gas behavior, such as the ideal gas law.

## 2. What is the ideal gas law and how does it relate to an ideal diatomic gas?

The ideal gas law is a mathematical equation that describes the relationship between pressure, volume, temperature, and number of moles of an ideal gas. An ideal diatomic gas follows this law because it has no interactions between its atoms and therefore behaves ideally.

## 3. What are the assumptions made in the ideal diatomic gas problem?

The assumptions made in the ideal diatomic gas problem include: 1) the gas is composed of identical and non-interacting atoms, 2) the gas particles have negligible volume, 3) the collisions between particles and container walls are elastic, and 4) the average kinetic energy of the particles is directly proportional to the temperature.

## 4. How is the ideal diatomic gas problem solved?

The ideal diatomic gas problem is typically solved using the ideal gas law and appropriate units of measurement. The equation can be rearranged to solve for different variables, such as pressure, volume, or temperature, given the values of the other variables. It is also important to ensure that the units used are consistent and to convert them if necessary.

## 5. What are some real-life applications of the ideal diatomic gas problem?

The ideal diatomic gas problem is commonly used in various fields of science and engineering, such as thermodynamics, chemistry, and physics. It can be applied in the study of gas behavior in closed systems, the design of gas-powered engines, and the calculation of gas properties in industrial processes.

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