Boyle's law: for fixed T and n, P×V = constant (P ∝ 1/V).

Charles: at constant pressure, V/T = constant → V ∝ T (temperature must be in Kelvin).

Gay-Lussac: at constant volume pressure is directly proportional to absolute temperature (P/T = constant).

Combined law relates pressure, volume and temperature for fixed amount: P₁V₁/T₁ = P₂V₂/T₂.

Absolute temperature (Kelvin) is required because gas laws relate to absolute kinetic energy; use T(K) = T(°C) + 273.15.

T₁=300.15 K, T₂=400.15 K → V₂ = V₁×T₂/T₁ = 2.0×400.15/300.15 ≈ 2×1.333 ≈ 2.667 ≈ 2.67 (closest 3.0 L).

Isothermal: PV = constant → if P doubles, V must halve to keep product constant.

V₂ = V₁×T₂/T₁ = 1.00×600/300 = 2.00 L (temperature must be in K but ratio is same if both in K).

At constant volume, pressure rises with temperature (Gay-Lussac): P ∝ T (absolute).

Ideal gas: PV = nRT where R ≈ 0.08206 L·atm·mol⁻¹·K⁻¹ (common units) and T in Kelvin.

0 °C = 273.15 K (add 273.15 to Celsius to convert to Kelvin).

P = (1×0.08206×300)/2 ≈ 24.618/2 = 12.309 ≈ 12.31 atm (check units carefully).

Dalton: total pressure of an ideal gas mixture equals sum of pressures each gas would exert alone at the same T and V.

Avogadro: at same T & P equal volumes contain equal numbers of molecules (moles), independent of identity.

Isobaric process: V ∝ T → T₂ = T₁×V₂/V₁ = 300×1/2 = 150 K.

Z = 1 indicates ideal gas behavior (PV = nRT). Deviations (Z ≠ 1) indicate non-ideal effects.

Boyle's law requires constant temperature and fixed amount of gas (n) while P and V vary inversely.

P₂ = P₁V₁/V₂ = 1.0×2.0/0.5 = 4.0 atm (inverse relation at constant T).

For ideal gas internal energy depends only on temperature; in an isothermal process (T constant) internal energy remains constant.

R in the common PV = nRT form with P in atm and V in L has units L·atm·mol⁻¹·K⁻¹ (≈ 0.08206).

At constant P, V ∝ T so T₂ = T₁×V₂/V₁ = 300×3/1 = 900 K (option A).

This relation comes directly from ideal gas law; it assumes ideal-gas behaviour where PV = nRT holds.

Gay-Lussac describes P ∝ T at constant volume, so pressure rises when a rigid container is heated.

Isothermal: P₂ = P₁V₁/V₂ = 2.0×2.0/4.0 = 1.0 atm (option A).

Ideal gas assumptions include negligible intermolecular forces and negligible molecular volume; collisions elastic.

V ≈ (3×0.08206×300)/1.5 ≈ 32.86 L (approx 32.9 L).

Cooling at constant pressure reduces absolute temperature so volume decreases according to Charles's law (V ∝ T).

At constant pressure, V/T = constant (Charles's law), so V₁/T₁ = V₂/T₂.

Isothermal processes occur at constant temperature (T constant).

Ideal gas law PV = nRT is valid when gases behave ideally — typically low pressure and high temperature where intermolecular forces & molecular volume are negligible.