Instructions: Enter exactly 3 values. Leave the field you want to calculate empty.
Result
function calculateIdealGas() {
// Retrieve input elements
var pInput = document.getElementById("pressure_p");
var vInput = document.getElementById("volume_v");
var nInput = document.getElementById("moles_n");
var tInput = document.getElementById("temp_t");
var rInput = document.getElementById("constant_r");
// Retrieve values (parse as float, empty strings become NaN)
var P = parseFloat(pInput.value);
var V = parseFloat(vInput.value);
var n = parseFloat(nInput.value);
var T = parseFloat(tInput.value);
var R = parseFloat(rInput.value);
// Result containers
var resultBox = document.getElementById("calc-result");
var resultValue = document.getElementById("result-value");
var resultSteps = document.getElementById("result-steps");
var errorBox = document.getElementById("calc-error");
// Reset display
resultBox.style.display = "none";
errorBox.style.display = "none";
errorBox.innerHTML = "";
// Identify which variable is missing (NaN)
var missingCount = 0;
var missingVar = "";
if (isNaN(P)) { missingCount++; missingVar = "P"; }
if (isNaN(V)) { missingCount++; missingVar = "V"; }
if (isNaN(n)) { missingCount++; missingVar = "n"; }
if (isNaN(T)) { missingCount++; missingVar = "T"; }
// Validation: R must be present
if (isNaN(R)) {
errorBox.innerHTML = "Error: Please specify the Gas Constant (R). Standard is 8.314.";
errorBox.style.display = "block";
return;
}
// Validation: Exactly one variable must be missing
if (missingCount !== 1) {
errorBox.innerHTML = "Error: Please enter exactly 3 values for P, V, n, and T. Leave exactly one field empty to solve for it.";
errorBox.style.display = "block";
return;
}
var calculatedValue = 0;
var unit = "";
var steps = "";
// Calculation Logic PV = nRT
if (missingVar === "P") {
// Solve for P = nRT / V
if (V === 0) {
errorBox.innerHTML = "Error: Volume cannot be zero.";
errorBox.style.display = "block";
return;
}
calculatedValue = (n * R * T) / V;
unit = "Pa";
steps = "Formula: P = (nRT) / V" +
"Substitution: P = (" + n + " × " + R + " × " + T + ") / " + V + "" +
"Calculation: P = " + (n * R * T).toFixed(2) + " / " + V;
}
else if (missingVar === "V") {
// Solve for V = nRT / P
if (P === 0) {
errorBox.innerHTML = "Error: Pressure cannot be zero.";
errorBox.style.display = "block";
return;
}
calculatedValue = (n * R * T) / P;
unit = "m³";
steps = "Formula: V = (nRT) / P" +
"Substitution: V = (" + n + " × " + R + " × " + T + ") / " + P + "" +
"Calculation: V = " + (n * R * T).toFixed(2) + " / " + P;
}
else if (missingVar === "n") {
// Solve for n = PV / RT
if (R * T === 0) {
errorBox.innerHTML = "Error: R and T must be non-zero.";
errorBox.style.display = "block";
return;
}
calculatedValue = (P * V) / (R * T);
unit = "mol";
steps = "Formula: n = (PV) / (RT)" +
"Substitution: n = (" + P + " × " + V + ") / (" + R + " × " + T + ")" +
"Calculation: n = " + (P * V).toFixed(2) + " / " + (R * T).toFixed(2);
}
else if (missingVar === "T") {
// Solve for T = PV / nR
if (n * R === 0) {
errorBox.innerHTML = "Error: n and R must be non-zero.";
errorBox.style.display = "block";
return;
}
calculatedValue = (P * V) / (n * R);
unit = "K";
steps = "Formula: T = (PV) / (nR)" +
"Substitution: T = (" + P + " × " + V + ") / (" + n + " × " + R + ")" +
"Calculation: T = " + (P * V).toFixed(2) + " / " + (n * R).toFixed(2);
}
// Display results
// Use toPrecision or toFixed based on magnitude for cleaner physics display
var displayVal = Math.abs(calculatedValue) 10000 ?
calculatedValue.toExponential(4) :
calculatedValue.toFixed(4);
resultValue.innerHTML = displayVal + " " + unit + "";
resultSteps.innerHTML = steps;
resultBox.style.display = "block";
}
Mastering AP Physics 2: Thermodynamics and the Ideal Gas Law
The AP Physics 2 curriculum spans a wide variety of advanced physics topics, including Fluid Mechanics, Thermodynamics, Electric Force, Field and Potential, Electric Circuits, Magnetism, Geometric and Physical Optics, and Quantum Physics. Among these, Thermodynamics is a cornerstone unit that frequently tests a student's ability to manipulate variables and understand the relationship between macroscopic properties of gases.
This calculator is designed specifically to assist with the Ideal Gas Law, a fundamental equation used throughout the course to model the behavior of an ideal gas under various conditions.
The Ideal Gas Law Equation
PV = nRT
Where the variables represent:
P (Pressure): The force exerted by the gas per unit area on the walls of its container. In SI units, this is measured in Pascals (Pa), where 1 Pa = 1 N/m². Note that AP exams often use atmospheres (atm), so conversion is key (1 atm = 101,325 Pa).
V (Volume): The 3D space occupied by the gas. The SI unit is cubic meters (m³). Be careful converting from Liters (L), as 1 m³ = 1000 L.
n (Moles): The amount of substance of the gas, measured in moles (mol).
R (Ideal Gas Constant): A physical constant that relates the energy scale to the temperature scale. The standard SI value is approximately 8.314 J/(mol·K).
T (Temperature): The absolute temperature of the gas. It MUST be in Kelvin (K) for the math to work. If you are given Celsius, add 273.15 to convert it ($K = ^\circ C + 273.15$).
Why Use an AP Physics 2 Calculator?
In an exam setting, you are provided with a reference table, but practicing with a tool like this helps build intuition for how changes in one variable affect the others. For example:
Isobaric Process: If Pressure (P) is constant, Volume (V) is directly proportional to Temperature (T). If you heat a gas, it expands.
Isothermal Process: If Temperature (T) is constant, Pressure (P) and Volume (V) are inversely proportional. Compressing a gas increases its pressure.
Isochoric Process: If Volume (V) is constant, Pressure (P) is directly proportional to Temperature (T). Heating a rigid container increases the internal pressure.
Common AP Physics 2 Conversion Pitfalls
The most common mistake students make on the AP Physics 2 exam regarding thermodynamics is unit inconsistency. The Ideal Gas Law requires a strict adherence to units based on the Gas Constant ($R$) used.
If you use $R = 8.314$, you must use:
Pa, m³, mol, K.
If you use $R = 0.08206$ (common in Chemistry but appears in Physics), you must use:
atm, L, mol, K.
This calculator utilizes the standard SI version ($R = 8.314$) which is the primary convention for physics equations involving energy and work. Always ensure your temperature is in Kelvin before calculating!