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#solid state physics

3 public questions tagged with this topic.

Zeroth Law Thermal Equilibrium and Quasi-static

What characteristic of a solid’s molecular structure leads to a molar specific heat capacity of approximately 3R ?

**Zeroth law of thermodynamics** if two systems A and B each in thermal equilibrium with third C, then A and B in equilibrium with each other, defines temperature as property that is same for systems in thermal equilibrium, basis for thermometer, temperature scale, thermal equilibrium means no net heat flow, same temperature. In solids, each atom vibrates with 3 degrees of freedom, contributing 3 k_B T (kinetic and potential) per atom. For a mole, this totals 3 R T , so C = (Δ U)/(Δ T) = 3R , due to vibrational motion. Using first law ΔU = Q - W, W = ∫ P

Ref: NCERT > Physics Book > Thermodynamics > Zeroth Law Thermal Equilibrium and Quasi-static

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RMS Speed and Temperature Dependence

A solid has a molar specific heat capacity of 24.5 J mol⁻¹ K⁻¹. How many degrees of freedom per atom does it have? (R =

**RMS speed** v_rms = √(3 R T/M) = √(3 k_B T/m) where M molar mass (kg/mol), m molecular mass (kg), k_B=1.38×10⁻²/³ J/K, R=8.314 J/mol·K, T absolute temperature (K). Proportional to √T and 1/√M, lighter gases faster at same T, e.g., H₂ faster than O₂, temperature increase raises v_rms as √T. C = f × (R)/(2), 24.5 = f × (8.31)/(2).f = (24.5 × 2)/(8.31) ≈ 5.9 ≈ 6. Substituting values gives 6, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > RMS Speed and Temperature Dependence

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Degrees of Freedom and Molar Specific Heat

A solid has a molar specific heat capacity of 24.9 J mol⁻¹ K⁻¹. What is the energy per degree of freedom per atom? (R =

**Molar specific heat** from equipartition C_v = f/2 R, C_p = f/2 R + R, γ = C_p/C_v =1+2/f, for f=3 γ=1.67, f=5 γ=1.4, f=6 γ=1.33, explaining specific heat variation with molecular structure, degrees of freedom determine heat capacity. C = f × (R)/(2), 24.9 = f × (8.31)/(2), f = (24.9 × 2)/(8.31) ≈ 6.Energy per degree of freedom = (1)/(2) k_B T, per mole = (1)/(2) R T.For 1 degree of freedom, energy per mole = (8.31)/(2) = 4.155 J mol⁻¹ K⁻¹ . Substituting values gives 4.16 J mol⁻¹ K⁻¹, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Degrees of Freedom and Molar Specific Heat

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