Question

In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5.Note that, unless explicitly stated, the variable γ should not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas.Part AFind an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0.Correctp(V) = p0(V0V)75Part BAt the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion.Express the work in terms of p0, V0, and V1. Your answer should not depend on temperature.Part CFind ΔU, the change of internal energy of the gas during the adiabatic expansion from volume V0 to volume V1.Express the change of internal energy in terms of p0, V0, and/or V1.Need Part B and C

Answer 1

The work done by the gas during an adiabatic expansion can be calculated with the formula W = p0V0[(V1/V0)^(1-γ) - 1] / (1-γ), and the change in internal energy of the gas is ΔU = -W.

Step-by-step explanation:

In an adiabatic expansion, the work done by the gas (W) can be calculated using the expression W = -(1/(γ-1))(p1V1 - p0V0), where γ (gamma) is the ratio of heat capacities (for a diatomic ideal gas, γ = 7/5), V0 and V1 are the initial and final volumes respectively, and p0 is the initial pressure. Since p(V) is already given, p1 can be obtained by substituting V1 into the p(V) equation. Plugging in these values, the work done by the gas during the adiabatic expansion from volume V0 to V1 is W = p0V0[(V1/V0)^(1-γ) - 1] / (1-γ).

In the case of the change in internal energy (ΔU), we utilize the first law of thermodynamics which states ΔU = Q - W, and for an adiabatic process Q = 0. Therefore, ΔU = -W. Hence, the change in internal energy of the gas during the adiabatic expansion is ΔU = -W = (1/(γ-1))(p1V1 - p0V0).

Answer 2

A: P=Po(Vo/V)^y

B: W=5/2Po(Vo-Vo^7/5 Vi^-2/5)

C: ∆V= 5/2Po[Vo^7/5 Vi^-2/5 -Vo]

Step-by-step explanation:

Attached is the solution