USAPhO 1998, Полуфинал — A1

1998 Exam 2 · 25 т.

1998 Exam 2 — INSTRUCTIONS

United States Physics Team

Entia non multiplicanda sunt praeter necessitatem

  1. DO NOT OPEN THIS TEST UNTIL YOU ARE GIVEN THE SIGNAL TO BEGIN.
  2. Work Part A first. You have 90 minutes to complete all four problems.
  3. After you have completed Part A, you may take a break.
  4. Then work Part B. You have 90 minutes to complete both problems.
  5. Show all work, as partial credit may be earned.
  6. Begin each problem on a fresh sheet of paper. In the upper right-hand corner of each page, write your name (last name first), the problem number, and the page number / total number of pages for that particular problem, for example:

Einstein, Albert

A2 - 3/4 for “Problem A2, page 3 of 4”

  1. A hand-held calculator may be used. Its memory must be cleared of data and programs. You may not use any books, notes, tables, or collections of formulas.
  2. Best wishes for an outstanding exam!
Possibly useful information
QuantityValue
Gravitational field at Earth’s surfaceg=9.8g=9.8 N/kg
Newton’s gravitational constantG=6.67×10−11G=6.67\times10^{-11} N·m2^2/kg2^2
Coulomb’s constantk=1/4πϵo=9×109k=1/4\pi\epsilon_o=9\times10^9 N·m2^2/C2^2
Biot-Savart constantkm=μo/4π=10−7k_m=\mu_o/4\pi=10^{-7} N·s2^2/C2^2
Speed of light in vacuumc=3×108c=3\times10^8 m/s
Boltzmann’s constantkB=1.38×10−23k_B=1.38\times10^{-23} J/K
Avogadro’s numberNA=6.02×1023N_A=6.02\times10^{23} mol−1^{-1}
Ideal gas constantR=NAkB=8.31R=N_Ak_B=8.31 J/mol-K
Elementary chargee=1.6×10−19e=1.6\times10^{-19} C
1 electron volt1 eV=1.6×10−191\text{ eV}=1.6\times10^{-19} J
Planck’s constanth=6.63×10−34 J⋅s=4.14×10−15 eV⋅sh=6.63\times10^{-34}\text{ J}\cdot\text{s}=4.14\times10^{-15}\text{ eV}\cdot\text{s}
Electron massm=9.1×10−31 kg=12 MeV/c2m=9.1\times10^{-31}\text{ kg}=\frac12\text{ MeV}/c^2
Binomial expansion(1+z)n≃1+nz(1+z)^n\simeq1+nz whenever ∣z∣≪1\lvert z\rvert\ll1
Small-angle approximationscos⁡θ≃1−12θ2\cos\theta\simeq1-\frac12\theta^2, sin⁡θ≃θ\sin\theta\simeq\theta whenever ∣θ∣≪1\lvert\theta\rvert\ll1

Copyright © 1998, AAPT

Условие

Two moles of monatomic ideal gas are taken through the reversible cycle shown on the PVPV diagram below. The cycle forms a rectangle, starting from State A at (Vo,Po)(V_o,P_o), to State B at (Vo,2Po)(V_o,2P_o), to State C at (2Vo,2Po)(2V_o,2P_o), to State D at (2Vo,Po)(2V_o,P_o), and back to State A. Express all answers to the following questions in terms of VoV_o, PoP_o, and the ideal gas constant RR.

Clockwise rectangular pressure-volume cycle A, B, C, D between Vo and2Vo and Po and2Po.

a. Calculate the net work done by the gas during the cycle. [5 т.]

b. Calculate the net heat transferred between the gas and the surroundings during one cycle. [5 т.]

c. Calculate cycle’s thermodynamic efficiency when operating as an engine. [10 т.]

d. Calculate the change in entropy of the gas as the system goes from State A to State D. [5 т.]

Решение

Оригинал в Архива: Semifinal 1998.pdf · официални решения: Semifinal 1998 Solutions.pdf