The Kelvin Formula for Thermopower

Thermoelectrics are important in physics, engineering, and material science due to their useful applications and inherent theoretical difficulty, especially in strongly correlated materials. Here we reexamine the framework for calculating the thermopower, inspired by ideas of Lord Kelvin from 1854. We find an approximate but concise expression, which we term as the Kelvin formula for the the Seebeck coefficient. According to this formula, the Seebeck coefficient is given as the particle number $N$ derivative of the entropy $\Sigma$, at constant volume $V$ and temperature $T$, $S_{\text{Kelvin}}=\frac{1}{q_e}\{\frac{\partial {\Sigma}}{\partial N} \}_{V,T}$. This formula is shown to be competitive compared to other approximations in various contexts including strongly correlated systems. We finally connect to a recent thermopower calculation for non-Abelian fractional quantum Hall states, where we point out that the Kelvin formula is exact.Comment: 6 pages, 2 figure

Atmospheric sampling of Supertyphoon Mireille with NASA DC-8 aircraft on September 27, 1991, during PEM-West A

The DC‐8 mission of September 27, 1991, was designed to sample air flowing into Typhoon Mireille in the boundary layer, air in the upper tropospheric eye region, and air emerging from the typhoon and ahead of the system, also in the upper troposphere. The objective was to find how a typhoon redistributes trace constituents in the West Pacific region and whether any such redistribution is important on the global scale. The boundary layer air (300 m), in a region to the SE of the eye, contained low mixing ratios of the tracer species O3, CO, C2H6, C2H2, C3H8, C6H6 and CS2 but high values of dimethylsulfide (DMS). The eye region relative to the boundary layer, showed somewhat elevated levels of CO, substantially increased levels of O3, CS2 and all nonmethane hydrocarbons (NMHCs), and somewhat reduced levels of DMS. Ahead of the eye, CO and the NMHCs remained unchanged, O3 and CS2 showed a modest decrease, and DMS showed a substantial decrease. There was no evidence from lidar cross sections of ozone for the downward entrainment of stratospheric air into the eye region; these sections show that low ozone values were measured in the troposphere. The DMS data suggest substantial entrainment of boundary layer air into the system, particularly into the eye wall region. Estimates of the DMS sulphur flux between the boundary layer and the free troposphere, based on computations of velocity potential and divergent winds, gave values of about 69 μg S m−2 d−1 averaged over a 17.5° grid square encompassing the typhoon. A few hours after sampling with the DC‐8, Mireille passed over Oki Island, just to the north of Japan, producing surface values of ozone of 5.5 ppbv. These O3 levels are consistent with the low tropospheric values found by lidar and are more typical of equatorial regions. We suggest that the central eye region may act like a Taylor column which has moved poleward from low latitudes. The high‐altitude photochemical environment within Typhoon Mireille was found to be quite active as evidenced by significant levels of measured gas phase H2O2 and CH3OOH and model‐computed levels of OH

Ozone production efficiencies of acetone and peroxides in the upper troposphere

HOx concentrations in the upper tropical troposphere can be enhanced by the presence of acetone and the convective injection of peroxides. These enhancements in HOx might be expected to increase ozone production by increasing the rate of the HO2+NO reaction. We show however that the convective enhancements of hydrogen peroxide (H2O2) and methyl hydroperoxide (CH3OOH) above steady state during the PEM West B campaign were largely restricted to air parcels of marine boundary layer origin in which the mean NO concentration was 8 pptv. The ozone production efficiencies of the two peroxides at such low NO concentrations are very small. Their impact on the ozone budget of the upper tropical troposphere during PEM West B was therefore probably modest. Unlike the peroxides, acetone in the upper tropical troposphere during PEM West B exhibited a positive correlation with NO. It also has a much larger ozone production efficiency than either H2O2 or CH3OOH. It therefore has a much greater potential for significantly increasing ozone production rates in the upper tropical troposphere

Comparisons of trace constituents from ground stations and the DC-8 aircraft during PEM-West B

Chemical data from ground stations in Asia and the North Pacific are compared with data from the DC-8 aircraft collected during the Pacific Exploratory Measurements in the Western Pacific Ocean (PEM-West B) mission. Ground station sampling took place on Hong Kong, Taiwan, Okinawa, and Cheju; and at three Pacific islands, Shemya, Midway, and Oahu. Aircraft samples were collected during 19 flights, most over the western North Pacific. Aluminum was used as an indicator of mineral aerosol, and even though the aircraft did sample Asian dust, strong dust storms were not encountered. The frequency distribution for non-sea-salt sulfate (nss SO4=) in the aircraft samples was bimodal: the higher concentration mode (∼1 μg m−3) evidently originated from pollution or, less likely, from volcanic sources, while the lower mode, with a peak at 0.040 μg m−3, probably was a product of biogenic emissions. In addition, the concentrations of aerosol sulfate varied strongly in the vertical: arithmetic mean SO4=concentrations above 5000 m ( = 0.21±0.69 μg m−3) were substantially lower than those below ( = 1.07±0.87 μg m−3), suggesting the predominance of the surface sources. Several samples collected in the stratosphere exhibited elevated SO4=, however, probably as a result of emissions from Mount Pinatubo. During some boundary layer legs on the DC-8, the concentrations of CO and O3 were comparable to those of clean marine air, but during other legs, several chemically distinct air masses were sampled, including polluted air in which O3was photochemically produced. In general, the continental outflow sampled from the aircraft was substantially diluted with respect to what was observed at the ground stations. Higher concentrations of aerosol species, O3, and CO at the Hong Kong ground station relative to the aircraft suggest that much of the continental outflow from southeastern Asia occurs in the lower troposphere, and extensive long-range transport out of this part of Asia is not expected. In comparison, materials emitted farther to the north apparently are more susceptible to long-range transport

Trace chemical measurements from the northern midlatitude lowermost stratosphere in early spring: Distributions, correlations, and fate

In situ measurements of a large number of trace chemicals from the midlatitude (37-57°N) lower stratosphere were performed with the NASA DC-8 aircraft during March 1994. Deepest penetrations into the stratosphere (550 ppb O3, 279 ppb N2O, and 350 K potential temperature) corresponded to a region that has been defined as the "lowermost stratosphere" (LS) by Holton et al [1995]. Analysis of data shows that the mixing ratios of long-lived tracer species (e. g. CH4, HNO3, NOy, CFCs) are linearly correlated with those of O3 and N2O. A ΔNOy/ΔO3 of 0.0054 ppb/ppb and ΔNOy/ΔN2O of -0.081 ppb/ppb is in good agreement with other reported measurements from the DC-8. These slopes are however, somewhat steeper than those reported from the ER-2 airborne studies. We find that the reactive nitrogen budget in the LS is largely balanced with HNO3 accounting for 80% of NOy, and PAN and NOx together accounting for 5%. A number of oxygenated species (e. g. acetone, H2O2) were present and may provide an important in situ source of HOx in the LS. SO2 mixing ratios were found to increase in the stratosphere at a rate that was comparable to the decline in OCS levels. No evidence of particle formation could be observed. Ethane, propane, and acetylene mixing ratios declined rapidly in the LS with Cl atoms likely playing a key role in this process. A number of reactive hydrocarbons/halocarbons (e. g. C6H6, CH3I) were present at low but measurable concentrations

59Co-NQR study on superconducting NaxCoO2.yH2O

Layered Co oxide NaxCoO2.yH2O with a superconducting transition temperature Tc =4.5 K has been studied by 59Co NQR. The nuclear spin relaxation rate 1/59T1 is nearly proportional to temperature T in the normal state. In the superconducting state, it exhibits the coherence peak and decreases with decreasing T below ~0.8Tc. Detailed comparison of the 1/T1T values and the magnetic susceptibilities between NaxCoO2.yH2O and NaxCoO2 implies that the metallic state of the former system is closer to a ferromagnetic phase than that of the latter. These experimental results impose a restriction on the mechanism of the superconductivity.Comment: 7 pages, 5 figures. to be published in J. Phys. Soc. Jpn. 72 (2003) No.

Photochemistry in the arctic free troposphere: Ozone budget and its dependence on nitrogen oxides and the production rate of free radicals

Abstract. Local ozone production and loss rates for the arctic free troposphere (58–85 ◦ N, 1–6 km, February–May) during the Tropospheric Ozone Production about the Spring Equinox (TOPSE) campaign were calculated using a constrained photochemical box model. Estimates were made to assess the importance of local photochemical ozone production relative to transport in accounting for the springtime maximum in arctic free tropospheric ozone. Ozone production and loss rates from our diel steady-state box model constrained by median observations were first compared to two point box models, one run to instantaneous steady-state and the other run to diel steady-state. A consistent picture of local ozone photochemistry was derived by all three box models suggesting that differences between the approaches were not critical. Our model-derived ozone production rates increased by a factor of 28 in the 1–3 km layer and a factor of 7 in the 3–6 km layer between February and May. The arctic ozone budget required net import of ozone into the arctic free troposphere throughout the campaign; however, the transport term exceeded the photochemical production only in the lower free troposphere (1–3 km) between February and March. Gross ozone production rates were calculated to increase linearly with NOx mixing ratios up to ∼300 pptv in February and for NOx mixing ratio

Kondo physics and orbital degeneracy interact to boost thermoelectrics on the nanoscale

We investigate the transport through a nanoscale device consisting of a degenerate double-orbital Anderson dot coupled to two uncorrelated leads. We determine the thermoelectric transport properties close to the one-electron regime and compare them to a corresponding single-orbital dot. The linear and nonlinear regimes are addressed, the latter via a non-equilibrium generalization of the non-crossing approximation based on the Keldysh formalism. Power output and efficiency in the Kondo regime are shown to be strongly enhanced through the presence of a second orbital. We predict an experimentally relevant optimal operating point which benefits from the concomitant increase of the Kondo temperature in the two-orbital setup. An approximation based on the transport coefficients and fulfilling the thermodynamic balance is proven to remain appropriate even far beyond the expected range of validity of such approaches. Finally, the double-orbital Kondo regime reveals itself as a promising candidate to avoid, at least partially, the generic dilemma between optimal thermoelectric efficiency on one hand, and fair power output on the other.Comment: 5 pages, 2 figure

Photochemistry in the arctic free troposphere: NOx budget and the role of odd nitrogen reservoir recycling

The budget of nitrogen oxides (NOx) in the arctic free troposphere is calculated with a constrained photochemical box model using aircraft observations from the Tropospheric O3 Production about the Spring Equinox (TOPSE) campaign between February and May. Peroxyacetic nitric anhydride (PAN) was observed to be the dominant odd nitrogen species (NOy) in the arctic free troposphere and showed a pronounced seasonal increase in mixing ratio. When constrained to observed acetaldehyde (CH3CHO) mixing ratios, the box model calculates unrealistically large net NOx losses due to PAN formation (62pptv/day for May, 1-3km). Thus, given our current understanding of atmospheric chemistry, these results cast doubt on the robustness of the CH3CHO observations during TOPSE. When CH3CHO was calculated to steady state in the box model, the net NOx loss to PAN was of comparable magnitude to the net NOx loss to HNO3 (NO2 reaction with OH) for spring conditions. During the winter, net NOx loss due to N2O5 hydrolysis dominates other NOx loss processes and is near saturation with respect to further increases in aerosol surface area concentration. NOx loss due to N2O5 hydrolysis is sensitive to latitude and month due to changes in diurnal photolysis (sharp day-night transitions in winter to continuous sun in spring for the arctic). Near NOx sources, HNO4 is a net sink for NOx; however, for more aged air masses HNO4 is a net source for NOx, largely countering the NOx loss to PAN, N2O5 and HNO3. Overall, HNO4 chemistry impacts the timing of NOx decay and O3 production; however, the cumulative impact on O3 and NOx mixing ratios after a 20-day trajectory is minimal. © 2003 Elsevier Science Ltd. All rights reserved

Coupled evolution of BrOx-ClOx-HOx-NOx chemistry during bromine-catalyzed ozone depletion events in the arctic boundary layer

Extensive chemical characterization of ozone (O3) depletion events in the Arctic boundary layer during the TOPSE aircraft mission in March–May 2000 enables analysis of the coupled chemical evolution of bromine (BrOx), chlorine (ClOx), hydrogen oxide (HOx) and nitrogen oxide (NOx) radicals during these events. We project the TOPSE observations onto an O3 chemical coordinate to construct a chronology of radical chemistry during O3 depletion events, and we compare this chronology to results from a photochemical model simulation. Comparison of observed trends in ethyne (oxidized by Br) and ethane (oxidized by Cl) indicates that ClOxchemistry is only active during the early stage of O3 depletion (O3 \u3e 10 ppbv). We attribute this result to the suppression of BrCl regeneration as O3 decreases. Formaldehyde and peroxy radical concentrations decline by factors of 4 and 2 respectively during O3 depletion and we explain both trends on the basis of the reaction of CH2O with Br. Observed NOx concentrations decline abruptly in the early stages of O3 depletion and recover as O3 drops below 10 ppbv. We attribute the initial decline to BrNO3 hydrolysis in aerosol, and the subsequent recovery to suppression of BrNO3 formation as O3 drops. Under halogen-free conditions we find that HNO4 heterogeneous chemistry could provide a major NOx sink not included in standard models. Halogen radical chemistry in the model can produce under realistic conditions an oscillatory system with a period of 3 days, which we believe is the fastest oscillation ever reported for a chemical system in the atmosphere