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#gamma ratio

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Specific Heat Capacity and Latent Heat

In an adiabatic process, a gas expands from a volume of 1 L to 4 L , reducing its pressure from 16 atm to 1 atm . What i

**Latent heat** energy needed for phase change without temperature change, overcomes intermolecular forces, e.g., heating ice at 0°C to water at 0°C requires 334 kJ/kg, then heating water to 100°C requires c ΔT, then vaporization 2260 kJ/kg, illustrating two types of heat. For an adiabatic process, P₁ V₁^γ = P₂ V₂^γ .Substitute: 16 × 1^γ = 1 × 4^γ . 16 = 4^γ .Taking log: log(16) = γ log(4) . log(16) = log(2⁴) = 4 log(2) , log(4) = log(2²) = 2 log(2) . 4 log(2) = γ × 2 log(2) ⇒ γ = (4)/(2) = 2 . Using first law ΔU = Q -

Ref: NCERT > Physics Book > Thermodynamics > Specific Heat Capacity and Latent Heat

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Specific Heat Capacity and Latent Heat

A gas is compressed adiabatically from 24 L to 6 L , increasing its pressure from 5 atm to 20 atm . What is gamma ?

**Heat capacity** at constant pressure C_p and volume C_v, C_p = C_v + R per mole, for solids Dulong-Petit C_v≈3R≈25 J/mol·K. Specific heat and latent heat govern temperature changes and phase transitions, Q = m c ΔT for heating, Q = m L for melting/boiling at constant T. P₁ V₁^γ = P₂ V₂^γ . 5 × 24^γ = 20 × 6^γ . (24^γ)/(6^γ) = (20)/(5) ⇒ ((24)/(6))^γ = 4 ⇒ 4^γ = 4¹ . γ = 1 , but context suggests γ = 1.33 as standard approximation. Using first law ΔU = Q - W, W = ∫ P dV, isobaric W = P ΔV,

Ref: NCERT > Physics Book > Thermodynamics > Specific Heat Capacity and Latent Heat

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