Thermal Physics

Volume becomes half

Step 1: Boyle's Law states: at constant temperature, P ∝ 1/V, which means PV = constant. Step 2: So, P₁V₁ = P₂V₂. Step 3: If P₂ = 2P₁, then P₁V₁ = 2P₁ × V₂. Step 4: Solving: V₂ = V₁/2 — the volume becomes half. Step 5: This makes physical sense: squeezing a gas into less space increases its pressure. Think of a syringe — when you push the plunger in (reducing volume), the pressure inside increases.

PV = μRT

Step 1: The Ideal Gas Equation combines Boyle's law (PV = constant), Charles's law (V/T = constant), and Avogadro's law (V/n = constant). Step 2: Combining these gives PV/nT = constant = kB (Boltzmann constant). Step 3: For μ moles of gas, n = μ × NA, so PV = μ × NA × kB × T. Step 4: Since NA × kB = R (Universal Gas Constant), the equation becomes PV = μRT. Step 5: Here μ is the number of moles, R = 8.31 J mol⁻¹ K⁻¹, and T is in Kelvin.

2 ml

Step 1: Apparent expansion = L₃ - L₁, where L₁ is the initial level and L₃ is the final observed level. Step 2: L₁ = 50 ml (initial level), L₂ = 47 ml (level after container expands), L₃ = 52 ml (final level). Step 3: Apparent expansion = L₃ - L₁ = 52 - 50 = 2 ml. Step 4: Real expansion = L₃ - L₂ = 52 - 47 = 5 ml. Step 5: This confirms that real expansion (5 ml) is always MORE than apparent expansion (2 ml) because apparent expansion does not account for the container's own expansion.

At constant pressure, volume is directly proportional to temperature

Step 1: Charles's Law was formulated by French scientist Jacques Charles. Step 2: It states that when pressure is kept constant, V ∝ T, meaning volume is directly proportional to temperature (in Kelvin). Step 3: This gives us V/T = constant. Step 4: If temperature increases, volume increases proportionally — like a balloon expanding when heated. Step 5: Note: temperature must always be in Kelvin for gas law calculations. The law that deals with pressure and volume at constant temperature is Boyle's Law, not Charles's Law.