Tools in This Collection
Heat Transfer Calculator
Calculate Q = mcΔT for heating and cooling problems
Gas Law Calculator
Solve ideal gas law PV = nRT and combined gas law
Wave Speed Calculator
Calculate wave speed, frequency, and wavelength
Decibel Distance Calculator
Calculate sound level changes with distance (inverse square law)
Thermodynamics and Wave Physics Workflow
Thermodynamics and wave problems share a common structure: identify the physical quantities (pressure, volume, temperature for gases; frequency, wavelength, amplitude for waves), select the right equation, and solve. Most gas law problems start with the ideal gas law, while heat transfer problems start with Q = mcΔT.
Ideal Gas Law: PV = nRT
The ideal gas law connects pressure (P in Pascals), volume (V in liters), moles of gas (n), the universal gas constant (R = 8.314 J/mol·K), and temperature (T in Kelvin). At standard temperature and pressure (0°C = 273.15 K, 1 atm = 101,325 Pa), one mole of ideal gas occupies exactly 22.4 liters. To find volume when pressure changes at constant temperature (Boyle's law): P₁V₁ = P₂V₂. If a gas at 1 atm occupies 10 L, compressing it to 2 atm gives 5 L. The Gas Law Calculator handles all ideal gas law and combined gas law problems.
Heat Transfer: Q = mcΔT
The heat transfer equation Q = mcΔT calculates the heat energy (Q in joules) needed to change the temperature of a mass (m in kg) with specific heat capacity (c in J/kg·K) by ΔT degrees. Water has c = 4,186 J/kg·K — the highest of common materials. Heating 1 liter (1 kg) of water from 20°C to 100°C requires Q = 1 × 4,186 × 80 = 334,880 J ≈ 335 kJ. Aluminum (c = 897 J/kg·K) heats up much faster — only 71.8 kJ for the same temperature rise. The Heat Transfer Calculator solves for any variable in this equation.
Wave Speed and Sound
Wave speed v = fλ, where f is frequency in Hz and λ is wavelength in meters. The speed of sound in air at 20°C is approximately 343 m/s. A 1,000 Hz tone has a wavelength of 343/1000 = 0.343 m (34.3 cm). At higher frequencies, wavelengths get shorter. The Wave Speed Calculator handles frequency, wavelength, and wave speed conversions for all wave types including sound and electromagnetic waves.
Decibel and Distance: Inverse Square Law
Sound intensity decreases by 6 dB for every doubling of distance from the source, following the inverse square law. A noise source measured at 80 dB at 1 meter will be 74 dB at 2 meters, 68 dB at 4 meters, and 62 dB at 8 meters. This predictable relationship is useful for estimating noise levels at different distances from machinery, speakers, or traffic. The Decibel Distance Calculator computes this relationship for any starting level and distance change.
Frequently Asked Questions
How do I apply the ideal gas law PV = nRT?
Identify which three of the five variables you know (P, V, n, R, T) and solve for the fourth. Remember R = 8.314 J/mol·K (or 0.08206 L·atm/mol·K if using atm and liters). Always convert temperature to Kelvin (K = °C + 273.15). For example, 2 moles of gas at 300 K and 1 atm: V = nRT/P = 2 × 0.08206 × 300 / 1 = 49.2 liters.
How do I calculate heat transfer for a temperature change?
Use Q = mcΔT where m is mass in kg, c is specific heat capacity in J/(kg·K), and ΔT is the temperature change in Celsius or Kelvin (same scale difference). Water c = 4,186 J/kg·K; steel c = 490 J/kg·K; aluminum c = 897 J/kg·K. Heating 0.5 kg of water by 50°C requires Q = 0.5 × 4,186 × 50 = 104,650 J ≈ 105 kJ.
Why does sound level drop 6 dB when distance doubles?
Sound radiates outward in a sphere from its source. When distance doubles, the surface area of that sphere increases by 4 times (A = 4πr²). Because the same energy spreads over 4 times the area, intensity drops to 1/4 — and since dB is a logarithmic scale, dividing intensity by 4 equals 10 × log(1/4) ≈ −6 dB. This is the inverse square law for point sources in open space.