Combined Gas Law Calculator

Find Final Temperature (T₂)

Enter the initial pressure, volume, and temperature, plus the final pressure and volume, and this calculator solves T₂ = P₂V₂T₁ / (P₁V₁) for you instantly.

Final Temperature Solver

Initial State
Final State
Final Temperature (T₂)

Deriving the Final Temperature Formula

Starting from the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, isolating T₂ gives:

T₂ = P₂V₂T₁ / (P₁V₁)

This is the formula to reach for whenever you know a gas's full initial state and its final pressure and volume, but need to work out how hot or cold it ended up. For example, predicting the temperature rise inside a bicycle pump as air is compressed into a smaller volume at higher pressure.

Note that the result is always computed on the absolute (Kelvin) scale internally, since that is the only scale on which the combined gas law's proportions hold true, and then converted to whichever unit you display it in.

State 1 → State 2 State 1 P₁, V₁, T₁ State 2 T₂ = ? P₂, V₂

Know everything about state 1 and the pressure/volume of state 2. Solve for the missing T₂.

Worked Example: Temperature After Compression

Problem: Gas at 1.00 atm, 8.00 L, and 290 K is compressed to 3.00 atm and 2.50 L. Find the final temperature T₂.

Given: P₁ = 1.00 atm, V₁ = 8.00 L, T₁ = 290 K, P₂ = 3.00 atm, V₂ = 2.50 L. T₂ = P₂V₂T₁ / (P₁V₁) T₂ = (3.00 × 2.50 × 290) / (1.00 × 8.00) T₂ ≈ 271.9 K (≈ −1.3°C)

Notice the final temperature is actually slightly lower than the starting 290 K, even though pressure tripled, because volume shrank by more than enough to offset the pressure increase. This is a good illustration of why intuition alone ("compressing gas heats it up") can mislead: only a full six-variable calculation like this one accounts for every effect at once.

Common Mistakes When Finding T₂

The most frequent mistake here is forgetting that T₁ must still be converted to Kelvin even though you're solving for a temperature. T₂ = P₂V₂T₁ / (P₁V₁) only has one temperature term, but it must be in Kelvin for the result to come out correctly, the calculator handles the display conversion back to °C or °F for you afterward.

A second mistake is mismatching pressure or volume units between the two states. Since both P₁/P₂ and V₁/V₂ effectively appear as ratios in this formula, an unconverted unit mismatch on either pair will scale the resulting temperature incorrectly.

A third pitfall is not sanity-checking the sign and magnitude of the result: if a gas is compressed into a smaller volume at higher pressure, intuition suggests temperature should rise, but as the worked example above shows, that isn't always true once both effects are combined precisely. Trust the calculation over intuition, but do double check that no inputs were swapped or mistyped if the result seems surprising.

Find Final Temperature FAQ

How do I find the final temperature of a gas?
Use the combined gas law rearranged for T₂: T₂ = P₂V₂T₁ / (P₁V₁). You need the initial pressure, volume, and temperature (P₁, V₁, T₁) plus the final pressure and volume (P₂, V₂). Enter all five into the calculator above and T₂ is computed instantly, in Kelvin, then converted to your chosen display unit.
Why does this calculator need five values instead of four?
Finding a final temperature from the combined gas law requires knowing both states almost completely, everything except the temperature you're solving for. That's five known quantities (P₁, V₁, T₁, P₂, V₂) to find the sixth (T₂). If you only have three values total, you likely want a single-law calculator like Boyle's, Charles', or Gay-Lussac's Law instead.
What if volume doesn't change between the two states?
If volume stays the same, you have an isochoric process and can use the simpler Gay-Lussac's Law calculator (P₁/T₁ = P₂/T₂) directly. It needs only three known values instead of five, since V cancels out entirely.
Can the answer come out in Celsius or Fahrenheit?
Yes: the calculator always solves internally in Kelvin (required for the proportion to be valid), then converts the result to whichever display unit you select for T₂: Kelvin, Celsius, Fahrenheit, or Rankine.
What units can I use for pressure and volume?
Pressure can be entered in Pa, kPa, MPa, bar, mbar, atm, mmHg, torr, psi, or inHg. Volume can be entered in m³, L, mL, cm³, dm³, ft³, in³, or gal (US). Mix units freely. The calculator converts everything internally before solving.
What is a typical scenario where I'd need to find T₂?
A common example: a fixed amount of gas is compressed from a known volume and pressure into a smaller container at a new pressure, and you need to know how hot it became as a result, useful for checking whether a compression process risks overheating a container or its contents.
Why might T₂ come out negative or unreasonably large?
A negative Kelvin temperature is physically impossible and always signals a data entry mistake, most often a pressure or volume unit mismatch between state 1 and state 2, or a value accidentally entered as zero or negative. Double-check that every input represents the same fixed quantity of gas and that units are consistent within each pair (P₁ with P₂, V₁ with V₂) before trusting the result.
How does this formula relate to compressing gas in an engine or pump?
Any time gas is compressed into a smaller volume at higher pressure, inside a bicycle pump, an air compressor, or an engine cylinder, this formula (or its adiabatic variant, if the compression happens too fast for heat to escape) predicts how hot the gas becomes as a direct result of that compression, which matters for material limits, lubrication, and combustion timing.
What if I already know T₂ and need to find T₁ instead?
This page is dedicated specifically to solving for T₂. To solve for T₁ (or any other one of the six combined gas law variables), use the interactive calculator on the homepage. It lets you leave any single variable blank, including T₁, and computes it from the other five using the rearranged formula T₁ = P₁V₁T₂ / (P₂V₂).

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