subject: Material Science

question:
Based on the data shown in the figure, estimate the specific micropore volume of the material using the Gurvich rule.
(Note: Assume the density of liquid nitrogen at 77 K is $\rho_{\text{liq}} \approx 0.808 \text{ g/cm}^3$, and the molar volume of gas is $V_m \approx 22414 \text{ cm}^3/\text{mol}$).

answer: Correct Answer: $0.031 \text{ cm}^3 \text{g}^{-1}$

analysis:
Analysis:Data Extraction: The Gurvich rule determines total micropore volume based on the saturation uptake at $P/P_0 \approx 1.0$. The maximum $N_2$ uptake at saturation is approximately $20 \text{ cm}^3 \text{g}^{-1}$.Calculation: Convert the gas volume (STP) to liquid volume using the given density and molar volume:$$V_p = 20 \times \frac{28.0134 \text{ (Molar Mass)}}{0.808 \times 22414} \approx 20 \times 0.001547 \approx \mathbf{0.031} \text{ cm}^3 \text{g}^{-1}
$$Why not $0.015$ incorrectly uses the uptake value at the isotherm's "knee" ($\approx 10 \text{ cm}^3 \text{g}^{-1}$), mistaking the monolayer capacity for the total pore volume.


subject: Chemistry

question:
Question:
In a Ni–Al dilute alloy with ballistic re-solution, the nucleation of γ′ (Ni₃Al) precipitates can be described by the quasi-free energy ΔG̅₀(R) as a function of the cluster radius R. The figure shows a single ΔG̅₀(R)–R curve, with three vertical dashed lines marking the radii P, Q, and R (the curve itself is not explicitly labeled as “stable/unstable”).
if a stationary point is a local maximum (dΔG̅₀/dR = 0 and d²ΔG̅₀/dR² < 0), it corresponds to an “unstable critical radius / barrier top”.
If a stationary point is a local minimum (dΔG̅₀/dR = 0 and d²ΔG̅₀/dR² > 0), it corresponds to a “stable size / attractor” (the stable precipitate size under irradiation).
Assume that the cluster-radius dynamics can be approximated by dR/dt ∝ − dΔG̅₀/dR (the system evolves in the direction of decreasing free energy).
Based on the figure (the shape of the curve near P and Q, and the relative heights of the curve at P, Q, and R), determine which of the following statements are correct:
A. P corresponds to a local maximum, so P is an unstable critical radius; if the initial radius R₀ is smaller than P, it will evolve toward larger R and tend toward Q.
B. Q corresponds to a local minimum, so Q is a stable equilibrium radius (an attractor); if R₀ is slightly perturbed away from Q (whether increased or decreased), the system will return to the vicinity of Q.
C. For any initial radius R₀ ∈ (P, Q) (between P and Q), we have dR/dt > 0, so the cluster will grow monotonically and eventually approach Q.
D. If the initial radius R₀ is to the left of P (R₀ < P), then the cluster will evolve toward smaller R (tending to dissolve/disappear), rather than spontaneously crossing P to form a stable precipitate.
E. From the figure one can read off that ΔG̅₀(P) > ΔG̅₀(Q), so the “barrier height” ΔG‡ = ΔG̅₀(P) − ΔG̅₀(Q) is positive.
F. Since R is located to the right of Q and the curve is increasing at R, we have dΔG̅₀/dR > 0 near R, hence dR/dt < 0; the radius will relax back to the left (toward Q).

answer: Correct Answer: B、D、E、F

analysis:
A (incorrect): Although P is a local maximum (top of the barrier, unstable), if R0 < P then on the left side of P the curve still increases with R (d\Delta\bar G_0/dR > 0). From dR/dt \propto -\,d\Delta\bar G_0/dR we obtain dR/dt < 0, so the radius decreases and tends to dissolve, rather than growing, crossing P, and going to Q.
B (correct): Q lies at the “bottom of the valley,” i.e., it is a local minimum (d\Delta\bar G_0/dR = 0, d^2\Delta\bar G_0/dR^2 > 0), so it is a stable attractor. To the left of Q the slope is negative, which makes dR/dt > 0; to the right of Q the slope is positive, which makes dR/dt < 0. Thus, on both sides the dynamics drive R back toward Q.
C (incorrect): When R0 \in (P, Q), the curve from P to Q is a descending branch, so d\Delta\bar G_0/dR < 0 \Rightarrow dR/dt > 0, and the radius grows to the right toward Q. However, although the statement “dR/dt > 0 everywhere in this interval” is correct locally for (P, Q), it implicitly suggests a global claim of “monotonic growth eventually approaching Q,” which is misleading: once R passes Q (to the right of Q), the sign flips and the dynamics pull it back, so “monotonic growth” cannot be stated as a global conclusion (it only holds inside that interval).
D (correct): To the left of P the curve is rising (d\Delta\bar G_0/dR > 0), hence dR/dt < 0, so the cluster evolves toward smaller R and tends to disappear. In a deterministic dynamics without noise/fluctuations it will not “spontaneously cross” the barrier at P.
E (correct): Reading from the graph, the energy at P is clearly higher than at Q (the peak lies above the valley), so \Delta\bar G_0(P) > \Delta\bar G_0(Q), and the barrier height \Delta G^\ddagger = \Delta\bar G_0(P) - \Delta\bar G_0(Q) is positive.
F (correct): R is located to the right of Q, and at R the curve is still on an ascending segment, so d\Delta\bar G_0/dR > 0 \Rightarrow dR/dt < 0. The radius therefore relaxes back to the left, evolving toward Q (the stable valley).


subject: Earth Science

question:
Qustion:
At the lowest pressure of 0.001 Torr, IFT (Information Field Theory) is used to perform Bayesian inversion of the temperature-profile field T(y) and the material thermal-conductivity function k(T). In the figure, the left panel shows the posterior of T(y) (solid blue line: median; blue shaded band: posterior uncertainty; “×”: data points; red dashed lines: samples). The right panel shows the posterior of k(T) (“×”: reference values; a vertical dashed line separates the data range from the extrapolation range).
Question: Based on the figure, which of the following statements are correct?
A. In the right panel, the vertical dashed line corresponds to a boundary temperature of approximately T = 1.3 × 10^3 K; the region to the left is labeled “data range,” and the region to the right is “extrapolation range.”
B. In the left panel, when the posterior median reaches T = 1000 K, the corresponding position is approximately y = 0.011–0.012 mm.
C. In the left panel, the uncertainty band is clearly wider around y = 0.003–0.006 mm, and becomes noticeably narrower for y > 0.02 mm.
D. In the right panel, within the data range, the reference values (“×”) show an overall systematic positive bias: most points lie above the posterior median curve (i.e., k_ref > k_median).
E. In the right panel, at T = 2000 K, the posterior median is approximately k_median = 0.20 W·m^−1·K^−1.
F. In the right panel, within the extrapolation range (to the right of the dashed line), the reference values (“×”) lie essentially all outside the blue uncertainty band, indicating that extrapolation fails completely.

answer: Correct Answer: A、B、C、D、E

analysis:
A (correct): In the right panel, the vertical dashed line is located at about T ≈ 1.3×10³ K; the region to the left of the dashed line is labeled “data range,” and the region to the right is labeled “extrapolation range,” which matches the description in the question.
B (correct): In the left panel, the median curve near T = 1000 K corresponds to a horizontal coordinate of about y ≈ 0.011–0.012 mm (by reading from the graph).
C (correct): In the left panel, the blue uncertainty band is clearly wider around y ≈ 0.003–0.006 mm and becomes obviously narrower for y > 0.02 mm, indicating that the uncertainty is larger in the middle range and that the tail region is better converged.
D (correct): In the right panel, within the data range (to the left of the dashed line), most of the reference values (×) lie above the median curve, showing an overall positive bias (k_{\rm ref} > k_{\rm median}).
E (correct): In the right panel at T ≈ 2000 K, the median curve reads about 0.20 W·m⁻¹·K⁻¹, which is consistent in order of magnitude with the statement in the question.
F (incorrect): In the right panel, within the extrapolation range (to the right of the dashed line), the reference values are not “mostly outside the uncertainty band”; on the contrary, most still fall within the shaded band or close to its boundary, so one cannot say that the extrapolation has “completely failed.”*


subject: Life Science

question:
Question:
The photographs below show three woodpeckers. Based on their appearance, identify the species or type of each woodpecker in the left, middle, and right images. You may select the same option for more than one image.

A) Syrian woodpecker
B) Hybrid woodpecker
C) Great-spotted woodpecker
D) Green woodpecker
E) Lesser spotted woodpecker
F) Pileated woodpecker
G) Northern flicker
H) Red-headed woodpecker

answer:
Correct Answer:
A(left), B(middle), C(right)

analysis:
Explanation:
These three birds look very similar, but there is a clear difference in the black facial markings (specifically the connection between the white cheek patch and the neck).

1. Right: Great Spotted Woodpecker
Characteristics: This is the standard Great Spotted Woodpecker.

Identification Point: The black line (malar stripe) extending from the base of the beak is "completely connected" to the black area on the back of the neck.

Result: This makes the white cheek patch appear as if it is enclosed inside a black frame.

2. Left: Syrian Woodpecker
Characteristics: A species very similar to the Great Spotted Woodpecker, found primarily in the Middle East and southeastern Europe.

Identification Point: The definitive difference from the Great Spotted Woodpecker is that the black line extending from the beak is "not connected (interrupted)" before it reaches the back of the neck.

Result: Because the black line is broken, the white cheek patch connects directly to the white feathers of the neck and shoulder (creating a continuous white passage).

3. Center: Hybrid
Characteristics: An individual born from the crossbreeding of a Syrian Woodpecker and a Great Spotted Woodpecker.

Identification Point: It displays characteristics intermediate between the two parents. In the individual in the photo, the black neck stripe is beginning to form, but it is not as thick or completely connected as that of the Great Spotted Woodpecker, or the pattern appears somewhat irregular—showing features that are neither fully one nor the other.

Summary The most important point to observe is the black line on the neck.

If it is connected → Great Spotted Woodpecker (Right)

If it is interrupted/broken → Syrian Woodpecker (Left)

If it is intermediate → Hybrid (Center)


subject: Astronomy

question:
Question:

The figure displays the stellar mass function (SMF) across different radial bins, stratified by redshift (Low-z vs High-z). Focusing on the three subplots in the innermost core region (\(0 < R \le 0.5 R_{500}\)), and based solely on the distribution patterns of the data points themselves, which of the following statements most accurately characterizes the true observed features of redshift evolution?

A. In the \(\log M_* \approx 9.3\text{–}9.8\) range, the points of the Low-z sample are systematically higher than those of the High-z sample overall, and this difference remains consistent across the three different binning methods, indicating that this mass range is the most sensitive to redshift evolution.

B. The two redshift samples show clear crossing behavior in the \(\log M_* \approx 10.2\text{–}10.6\) range (in some bins High-z is higher than Low-z, in others the opposite), suggesting that the shape evolution of the SMF in this range is non-monotonic.

C. All three subplots show that at \(\log M_* > 11.0\), the error bars for Low-z and High-z data points are markedly asymmetric, with the lower error limits of Low-z generally larger than the upper error limits.

D.In the leftmost panel, the High-z sample exhibits greater scatter (dispersion among points) at the low-mass end rather than a systematic shift, implying that visual inspection alone cannot robustly support a monotonic evolutionary trend at the low-mass end.

answer: Correct Answer: A

analysis:
Explanation:
From the three subplots corresponding to the innermost radial interval ( \(0 < R \le 0.5 R_{500}\) ), it can be observed that in the low-mass range of \(\log M_* \approx 9.3\)–\(9.8\), the low-redshift sample (Low‑z, represented by blue data points) consistently lies above the high-redshift sample (High‑z, red data points) under all three binning schemes. Moreover, this difference exceeds or approaches the extent of the error bars in most mass bins, indicating a stable and consistent offset. This demonstrates that this mass range is most sensitive to redshift evolution, reflecting an increase in the relative abundance of dwarf galaxies in the core region as cosmic time progresses. In contrast, in the intermediate- to high-mass range ( \(\log M_* \gtrsim 10.2\) ), the two datasets largely overlap and do not exhibit a clear systematic separation; the error bars are generally symmetric and show no prominent asymmetric statistical features. Therefore, only option A accurately summarizes the principal observational trend revealed by the figure.