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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Work (P - V)
P1V1 - P2V2 / (? - 1)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
1/2 CV²
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2

2. Helmholtz Free Energy
U - ts = -tlog(Z)
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
Braking Radiation
J = ? Fdt

3. Atom: Hydrogen Wave Function Type
NC?T
Exponentially decreasing radial function
µ0 I1I2 / (2pd)
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

4. Biot-Savart law
<?1|?2> = 0 ? Orthogonal
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
I = I_cm + md²
dQ = dW +dU

5. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
?mc²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

6. td(entropy) =
F = s * T4
PdV +dU
U - ts = -tlog(Z)
?= h/v(2mE)

7. First law of thermodynamics (explain direction of energy for each term)
ds² = (c*dt)² - ?(x_i)²
V = V0 + V0 a ?T
Always Real
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

8. Energy levels from the Coulomb potential
? (t-vx/c²)
Hbar*?³/(p²c³exp(hbar?/t)-1)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

9. Resistance - length - area - rho
E = <?| H |?>
?s = 0 - ?l = ±1
X_L = i?L
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

10. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
?mc²
E²-p²c²
B = µ0 I n

11. Poisson distribution (µ and s)
u dm/dt
(3/2) n R ?t
µ=s^2
I = -(c ?t)^2 + d^2

12. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
DS = 0 - dQ = 0 - P V^? = constant
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Cv = dE/dT = 3R
?mc²

13. Bernoulli Equation
?? = h/mc * (1-cos(?))
P +1/2 ? v² + ?gh = Constant
L = mr²d?/dt
(° of Freedom)kT/2

14. Quant: Orthogonality of States
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
<?|O|?>
<?1|?2> = 0 ? Orthogonal
?= h/v(2mE)

15. Relativistic interval (which must remain constant for two events)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Faraday/Lenz: current inducted opposes the changing field
I = -(c ?t)^2 + d^2
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

16. Perpendicular axis theorem
1/ne - where n is charge carrier density
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? (t-vx/c²)
I_z = I_x + I_y (think hoop symmetry)

17. SR: Spacetime Interval
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Exp(N(µ-e)/t)
ds² = (c*dt)² - ?(x_i)²
P1V1 - P2V2 / (? - 1)

18. Relativistic Energy
Measurements close to true value
?mc²
<T> = -<V>/2
L = L_0 Sqrt[1-v^2/c^2]

19. Current in resistor in RC circuit
Isentropic
I = V/R exp(-t/RC)
C_eq = ?C_i
NC?T

20. Resonance frequency of LC circuit
dQ = dW +dU
E = s/e_0
Int ( A . dr) = Int ( del x A) dSurface
1/vLC

21. Charge in Capacitor
Q = CVexp(-t/RC)
Exponentially decreasing radial function
DS = 0 - dQ = 0 - P V^? = constant
v(mean)

22. Thin Film Theory: Constructive / Destructive Interference
Const: 2t = (n +.5)? Destructive 2t = n?
P/A = s T^4
F = s * T4
Opposing charge induced upon conductor

23. EM: Bremsstrahlung (translation)
0
? = 1.22? / d
Braking Radiation
J/(ne) n: atom density

24. Angular momentum operators L^2 and L_z
L = L_0 Sqrt[1-v^2/c^2]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

25. Selection rules for atomic transitions
Exp(N(µ-e)/t)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

26. Magnetic Field of a long solenoid
<?|O|?>
B = µ0 I n
I = I_cm + (1/2)m d^2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

27. Source-free RC Circuit
Infinitely close to equilibrium at all times
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
µ0 I / 2pR
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

28. Stoke'S Theorem
Int ( A . dr) = Int ( del x A) dSurface
Always Real
P/A = s T^4
I_z = I_x + I_y (think hoop symmetry)

29. EM: Electromagnetic inertia
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Cv = dE/dT = 3R
Faraday/Lenz: current inducted opposes the changing field
F = qv×B

30. Thermo: Adiabatic Work vs Isothermal Work
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
4H + 2e- ? He +2? + 6?
H = H_0 + ?H
W_A < W_I

31. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
C_eq = ?C_i
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
DW = P dV

32. Atom: Orbital Config
L = T - V dL/dq = d/dt dL/dqdot
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
E = s/e_0
X_L = i?L

33. Astro: Kepler'S Third Law
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
P² ~ R³
Z²/n² (m_red/m_elec)
1/2 CV²

34. EM: Parallel Capacitance
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
C_eq = ?C_i
Cv = dE/dT = 3R

35. Wein'S Displacement Law
M? = 2dsin(?)
µ = m_e/2
Isentropic
?max = 2.898 x 10 -³ / T

36. Heat added
F = I L X B
Z_c = -i/(?C) ; Z_L = i ? L
NC?T
T^2 = k R^3 - k=constant

37. Entropy (# of states - and in terms of other thermo quantities)
T = I?²/2
?? = h/mc * (1-cos(?))
S = k ln[O] ; dS = dQ/T
DW/dq

38. QM: de Broglie Wavelength
?= h/v(2mE)
F = s * T4
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
I_z = I_x + I_y (think hoop symmetry)

39. Wein'S displacement law for blackbodies (? and T)
?_max = b/T
µ0 I1I2 / (2pd)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Measurements close to mean

40. Quant: Commutator Relation [AB -C]
J/(ne) n: atom density
W_A < W_I
P/A = s T^4
A[B -C] + [A -C]B

41. Selection Rules
T^2 = k R^3 - k=constant
?s = 0 - ?l = ±1
u dm/dt
B = µ0 I n

42. SR: Total Energy of a Particle
Z_c = -i/(?C) ; Z_L = i ? L
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Opposing charge induced upon conductor
F = qv×B

43. De Broigle Wavelength
B = µ0 I n
Q = CVexp(-t/RC)
Isentropic
? = h/mv

44. Mech: Impulse
F = qv×B
PdV +dU
J = ? Fdt
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

45. EM: Maxwell'S equations
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
?? = h/mc * (1-cos(?))
H = H_0 + ?H
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

46. Polarizers - intensity when crossed at ?
NC?T
Asin(?) = m?
Q = CVexp(-t/RC)
I = I_0 Cos[?]^2

47. Dulong Petit Law
Q = CVexp(-t/RC)
PdV +dU
F_f = µ*F_N
Cv = dE/dT = 3R

48. Volumetric Expansion
P/A = s T^4
Sin(?) = ?/d
V = V0 + V0 a ?T
J = ? Fdt

49. Clausius-Clapeyron Equation
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Sin(?) = ?/d
Dp/dt = L / (t ?V)

50. Magnetic Dipole Moment and Torque
Q = CVexp(-t/RC)
µ = Current * Area T = µ x B
? = h/p
µ = m_e/2