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Obtain the dimensions of (1) coefficient of thermal conductivity (2) Gas constant (3) Boltzmann constant (4) Planck's constant. |
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Answer» Solution :Dimensions of TEMPERATURE `=[K]` 1. COEFFICIENT of thermal conductivity `K=(Qx)/(A(T_(1)-T_(2))t)` Q- heat ENERGY x- distance , A-area of cross section `T_(1),T_(2)` temperature t-time Dimension of K`=([ML^(2)T^(-2)][L])/([L^(2)][K][T])` `=[MLT^(-3)K^(-1)]` 3. Gas constnat `R=PV//T`, where T is for temperature Dimensions of `R=([ML^(-1)T^(-2)][L^(3)])/([K])` `=[ML^(2)T^(-2)K^(-1)]` 3. Boltzmann constant k, energy `=3//2kT` `k=("Dimensions of Energy ")/("Dimensions of TEMP")` `=([ML^(2)T^(-2)])/([K])` `=[ML^(2)T^(_2)K^(-1)]` 4. Planck.s constnat H `E=hv,h=E/v,` E for energy and v for frequency `h=([ML^(2)T^(-2)])/([T^(-1)])=[ML^(2)T^(-1)]` |
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