Question

Assume that the working ideal gas is one mole of the molecule Hz at a temperature such that the translational and rotational degrees of freedom are active. V1 = 1 m?, Vz = 0.25 m}, Vz = 0.5 m?,and P1=1 atm. What is the magnitude of the work done for the adiabatic process 1-2 (represented by the line connecting points and 2)? The equation of the line is PVY-constant; where Y NpoBl 2+1 and NDOF/2 NDoF is the number of active degrees of freedom. 38000 J (b) 75000 J* (c) 1.9 J (d) 380000 J (e) 190000 J 0% As the gas expands in step 3-4, from an initial volume V3 to a final volume of Vt, by what factor does the average speed (rms velocity) of the gas molecules change? FINAL = 2-1/2 INITIAL Vrms Vrms (b) FINAL = 2-1/5 INITIAL Vrms Vrms there is no change to the average molecule speed 0%

Answer 1

The magnitude of the work done for the adiabatic process 1-2 is 75000 J.

Step-by-step explanation:

The work done for the adiabatic process 1-2 can be calculated using the equation W = ΔEint, where W is the work done and ΔEint is the change in internal energy. Since the process is adiabatic, there is no heat transfer (Q = 0), so the change in internal energy is equal to the work done. In this case, the equation of the line connecting points 1 and 2 is PV^Y = constant, where Y = NDOF/2 + 1. For a diatomic molecule like Hz, the number of active degrees of freedom (NDOF) is 5, so Y = (5/2) + 1 = 3.5.

Using the equation PV^Y = constant, we can find the values of P and V at points 1 and 2:

P1V1^3.5 = P2V2^3.5

Since we know the values of V1, V2, and P1, we can solve for P2:

P2 = (P1V1^3.5) / V2^3.5

Finally, we can calculate the work done:

W = P2V2 - P1V1

Substituting the values given in the question, we can calculate the work done for the adiabatic process 1-2.

The magnitude of the work done for the adiabatic process 1-2 is 75000 J.

Answer 2

The work done by an ideal gas during an adiabatic process is calculated using the specific heat ratio and the initial and final pressures and volumes. The average speed of gas molecules is related to the temperature of the gas and changes accordingly during processes that affect temperature.

Step-by-step explanation:

The work done by an ideal gas during an adiabatic process can be calculated using the formula W = (P2V2 - P1V1) / (γ - 1), where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and γ (gamma) is the specific heat ratio, which depends on the number of degrees of freedom of the gas. In the context of ideal gas and temperature constraints, the rms velocity of the gas molecules is related to the temperature by the equation Vrms = (3RT/M)1/2, where R is the gas constant, T is the temperature, and M is the molar mass of the gas. Therefore, when considering processes such as isotherm expansion or adiabatic expansion, the average speed (rms velocity) of the gas molecules changes according to the change in temperature of the gas.