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

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

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

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

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

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 of HOx in the upper troposphere at northern midlatitudes

The factors controlling the concentrations of HOx radicals (= OH + peroxy) in the upper troposphere (8-12 km) are examined using concurrent aircraft observations of OH, HO2, H2O2, CH3OOH, and CH2O made during the Subsonic Assessment Ozone and Nitrogen Oxide Experiment (SONEX) at northern midlatitudes in the fall. These observations, complemented by concurrent measurements of O3, H2O, NO, peroxyacetyl nitrate (PAN), HNO3, CH4, CO, acetone, hydrocarbons, actinic fluxes, and aerosols, allow a highly constrained mass balance analysis of HOx and of the larger chemical family HOy (= HOx + 2 H2O2 + 2 CH3OOH + HNO2 + HNO4). Observations of OH and HO2 are successfully simulated to within 40% by a diel steady state model constrained with observed H2O2 and CH3OOH. The model captures 85% of the observed HOx variance, which is driven mainly by the concentrations of NOx (= NO + NO2) and by the strength of the HOx primary sources. Exceptions to the good agreement between modeled and observed HOx are at sunrise and sunset, where the model is too low by factors of 2-5, and inside cirrus clouds, where the model is too high by factors of 1.2-2. Heterogeneous conversion of NO2 to HONO on aerosols (γNO2=10-3) during the night followed by photolysis of HONO could explain part of the discrepancy at sunrise. Heterogeneous loss of HO2 on ice crystals (γice_HO2=0.025) could explain the discrepancy in cirrus. Primary sources of HOx from O(1D)+H2O and acetone photolysis were of comparable magnitude during SONEX. The dominant sinks of HOy were OH+HO2 (NOx<50 parts per trillion by volume (pptv)) and OH+HNO4 (NOx>50 pptv). Observed H2O2 concentrations are reproduced by model calculations to within 50% if one allows in the model for heterogeneous conversion of HO2 to H2O2 on aerosols (γHO2=0.2). Observed CH3OOH concentrations are underestimated by a factor of 2 on average. Observed CH2O concentrations were usually below the 50 pptv detection limit, consistent with model results; however, frequent occurrences of high values in the observations (up to 350 pptv) are not captured by the model. These high values are correlated with high CH3OH and with cirrus clouds. Heterogeneous oxidation of CH3OH to CH2O on aerosols or ice crystals might provide an explanation (γice_CH3OH∼0.01 would be needed). Copyright 2000 by the American Geophysical Union