Gay-Lussac'ss Law Calculator
Calculate gay-lussac's law calculator calculate final gas pressure P2 or temperature T2 under constant volume using Gay-Lussac's Law (P1 / T1 = P2 / T2). Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Isochoric Gas Pressure (P_1 / T_1 = P_2 / T_2)
Enter your physical parameters below to compute verified isochoric gas metrics.
Calculation Results
Calculated using verified physical methodology: Gay-Lussac's Law: \P_1 / T_1 = \P_2 / T_2 \implies P_2 = P_1 \left(\frac{T_{2,K}}{T_{1,K}}\right)
\text{Isochoric State Constant: } k = \P / T
Quick Summary
The Gay-Lussac's Law Calculator evaluates isochoric thermal pressure increase ($\P_1 / T_1 = \P_2 / T_2$), computing final pressure ($P_2 = P_1 \frac{T_{2,K}}{T_{1,K}}$) in Kilopascals (kPa), atm, bar, and Imperial PSI.
Formula Explanation
Gay-Lussac's Law: \P_1 / T_1 = \P_2 / T_2 \implies P_2 = P_1 \left(\frac{T_{2,K}}{T_{1,K}}\right)
\text{Isochoric State Constant: } k = \P / T
How It Works
The Gay-Lussac's Law Calculator converts temperatures ($T_1, T_2$) to Kelvin ($T_K = T_C + 273.15$). It multiplies initial pressure ($P_1$) by final Kelvin temperature ($T_{2,K}$) and divides by initial Kelvin temperature ($T_{1,K}$). It outputs final pressure ($P_2$) in kPa, atm, bar, Imperial PSI, and percentage pressure increase.
Step-by-Step Worked Example
Practical Problem: Gas inside a rigid steel tank at $P_1 = 200.0\text{ kPa}$ and $T_1 = 20.0^\circ\text{C}$ is heated to $T_2 = 80.0^\circ\text{C}$. Calculate final pressure $P_2$.
- Step 1: Identify Input Parameters: $P_1 = 200.0\text{ kPa}$, $T_1 = 20.0^\circ\text{C}$, $T_2 = 80.0^\circ\text{C}$.
- Step 2: Convert Temperatures to Absolute Kelvin: $T_{1,K} = 20.0 + 273.15 = 293.15\text{ K}$; $T_{2,K} = 80.0 + 273.15 = 353.15\text{ K}$.
- Step 3: Calculate Kelvin Temperature Ratio ($T_2 / T_1$): $\text{Ratio} = \353.15 / 293.15 = 1.20467\text{ (1.205x temperature ratio)}$.
- Step 4: Apply Gay-Lussac's Law Formula ($P_2 = P_1 \T_2 / T_1$): $P_2 = 200.0\text{ kPa} \times 1.20467 = 240.93\text{ kPa}$.
- Step 5: Convert and Interpret Final Pressure Units: Final Pressure $P_2 = 240.93\text{ kPa} = 2.378\text{ atm} = 2.409\text{ bar} = 34.94\text{ PSI}$. Thermal pressure increase = $+20.47\%$.
Real-World Calculation Examples
Scenario 1: Rigid Steel Tank Heating (20°C to 80°C)
Parameters: $P_1 = 200\text{ kPa}$, $T_1 = 20^\circ\text{C}$, $T_2 = 80^\circ\text{C}$
Result: $P_2 = 240.93\text{ kPa}$ (34.94 PSI, $+20.47\%$ pressure rise). Rigid tank heating.
Scenario 2: Automobile Tire Driving Heat (20°C to 50°C)
Parameters: $P_1 = 220\text{ kPa}$ (32 PSI gauge), $T_1 = 20^\circ\text{C}$ (293.15 K), $T_2 = 50^\circ\text{C}$ (323.15 K)
Result: $P_2 = 242.53\text{ kPa}$ (35.18 PSI gauge). Highway tire heating pressure spike.
Scenario 3: Pressure Cooker Steam Pressure (20°C to 120°C)
Parameters: $P_1 = 101.3\text{ kPa}$ (1 atm), $T_1 = 20^\circ\text{C}$, $T_2 = 120^\circ\text{C}$ (393.15 K)
Result: $P_2 = 135.87\text{ kPa}$ (1.341 atm, 19.71 PSI). Pressure cooker internal rise.
Scenario 4: Aerosol Can Fire Exposure (20°C to 400°C)
Parameters: $P_1 = 300\text{ kPa}$, $T_1 = 20^\circ\text{C}$ (293.15 K), $T_2 = 400^\circ\text{C}$ (673.15 K)
Result: $P_2 = 688.88\text{ kPa}$ (6.80 atm, 99.91 PSI). Aerosol explosion hazard.
Key Benefits of Using This Calculator
Isochoric Process Model
Accurately models constant-volume thermal pressure increases ($P \propto T_K$) in rigid containers.
Pressure Vessel & Tire Safety
Essential for calculating tire pressure changes and industrial boiler explosion thresholds.
Multi-Unit Readouts
Outputs final pressure in kPa, atm, bar, and Imperial PSI ($\text{lb/in}^2$).
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is Gay-Lussac's Law?
Gay-Lussac's Law (Amontons' Law) states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature in Kelvin (P1 / T1 = P2 / T2).
What is the formula for Gay-Lussac's Law?
P1 / T1 = P2 / T2, or P2 = P1 * (T2 / T1) using absolute Kelvin temperatures.
Who discovered Gay-Lussac's Law?
French chemist Joseph Louis Gay-Lussac published it in 1808, building on earlier work by Guillaume Amontons in 1702.
What is an isochoric process?
An isochoric (or isometric/isovolumetric) process is a thermodynamic process during which volume remains strictly constant (delta V = 0).
Why do car tire pressures increase after long highway driving?
Tire friction heats the enclosed air inside the tire (V = constant); per Gay-Lussac's Law, higher temperature T increases internal tire pressure P by ~2 to 5 PSI.
Why do aerosol cans carry "Do Not Incinerate" warning labels?
Heating an enclosed aerosol can (constant volume V) causes pressure P to skyrocket (Gay-Lussac's Law), exceeding structural seam strength and causing an explosive rupture.
What happens to gas pressure when Kelvin temperature is doubled?
Pressure DOUBLES (P2 = 2 * P1).
How does a pressure cooker work using Gay-Lussac's Law?
A sealed pressure cooker traps steam at constant volume; heating raises steam temperature T, which increases internal pressure P, raising water's boiling point above 100°C for faster cooking.
Is work done in an isochoric gas process?
No! Boundary work W = integral(P dV) = 0 because volume change dV is zero.
Why must temperatures be in Kelvin?
Because molecular kinetic energy and thermal pressure scale from absolute zero (0 K); using Celsius would yield incorrect ratios or negative pressures.