Sublimation Pressure of Ice Calculator at 15 C
Use a physics based model to estimate the equilibrium vapor pressure over ice. Enter temperature, select equation method, choose output units, and generate a pressure curve with Chart.js.
Result
Press the calculate button to compute the sublimation pressure of ice.
Expert Guide: How to Calculate the Sublimation Pressure of Ice at 15 C
Sublimation pressure of ice is the equilibrium vapor pressure above a solid ice surface. It is central in meteorology, cryogenic engineering, vacuum systems, planetary science, freeze drying, and cold region process modeling. If you are trying to calculate the sublimation pressure of ice at 15 C, the first thing to understand is that 15 C is above the normal melting point of ice at standard pressure. That means stable bulk ice does not generally persist there in equilibrium with vapor alone. Even so, scientists and engineers still perform the calculation because it is useful as a mathematical extrapolation, and it can also approximate short lived or constrained conditions where local ice surfaces exist.
In practice, you can calculate a pressure value using established empirical equations. The calculator above supports two methods: a high quality Murphy and Koop ice equation and a simpler Clausius Clapeyron style approximation. The Murphy and Koop relation is widely used in atmospheric science for vapor pressure over ice and is known for strong accuracy in the subzero region where ice is physically stable. At 15 C, using that same equation is technically outside its most trusted range, but still useful to illustrate trend behavior and to compare against vapor pressure over liquid water.
What sublimation pressure means physically
Sublimation is the phase transition directly from solid to vapor. The sublimation pressure is the vapor pressure at which the rates of sublimation and deposition are equal for ice. If ambient partial pressure of water vapor is lower than this equilibrium pressure, net sublimation occurs. If ambient partial pressure is higher, deposition or frost growth can occur. This is why sublimation pressure matters in snowpack dynamics, freezer burn, spacecraft thermal design, and high altitude cloud microphysics.
- Low ambient vapor pressure relative to equilibrium over ice drives mass loss from ice.
- Temperature is the dominant control because equilibrium pressure rises rapidly with warming.
- Even small temperature changes can create large percentage changes in sublimation rate potential.
Core equations used in engineering calculations
The first equation implemented in the calculator is the Murphy and Koop vapor pressure over ice expression:
ln(P) = 9.550426 – 5723.265 / T + 3.53068 ln(T) – 0.00728332 T
where T is in kelvin and P is in pascals. This relation is commonly cited for cold atmospheric conditions and is often used in cloud and climate models.
The second equation is a Clausius Clapeyron style approximation:
P = P0 * exp((Ls / Rv) * (1 / T0 – 1 / T))
with typical constants P0 = 611.657 Pa at T0 = 273.16 K, latent heat of sublimation Ls around 2.834e6 J/kg, and water vapor gas constant Rv around 461.5 J/(kg K). This method is intuitive and very useful for quick calculations, although it is less accurate over wide ranges because latent heat is treated as constant.
Important interpretation at 15 C
At 15 C, liquid water is the stable phase under normal atmospheric pressure. So why calculate sublimation pressure of ice there? There are three common reasons:
- To demonstrate exponential pressure temperature sensitivity and model behavior.
- To compare equilibrium over ice versus over liquid in phase transition studies.
- To evaluate constrained systems where small ice inclusions transiently exist above 0 C.
In other words, the value can still be mathematically meaningful, even if macroscopic ice is not thermodynamically stable in everyday open conditions at 15 C.
Reference data table: equilibrium pressure over ice by temperature
The following values are representative results from a Murphy and Koop style calculation and are consistent with standard atmospheric thermodynamic trends. These numbers are useful as engineering checkpoints when validating a calculator.
| Temperature (C) | Temperature (K) | Equilibrium vapor pressure over ice (Pa) | Approximate pressure (hPa) |
|---|---|---|---|
| -40 | 233.15 | 12.8 | 0.128 |
| -30 | 243.15 | 38.0 | 0.380 |
| -20 | 253.15 | 103.3 | 1.033 |
| -15 | 258.15 | 165.3 | 1.653 |
| -10 | 263.15 | 259.9 | 2.599 |
| 0 | 273.15 | 611.2 | 6.112 |
| 15 | 288.15 | 1705.0 | 17.05 |
Comparison table: over ice versus over liquid water
Around freezing, vapor pressure over liquid water is slightly higher than over ice at the same temperature below 0 C. This difference drives important cloud microphysics effects, including the Bergeron Findeisen growth mechanism in mixed phase clouds. At 15 C the liquid saturation value is the standard reference, while an over ice value is mainly extrapolative.
| Temperature (C) | Over ice (Pa) | Over liquid water (Pa) | Relative difference |
|---|---|---|---|
| -20 | 103 | 125 | Liquid about 21% higher |
| -10 | 260 | 286 | Liquid about 10% higher |
| -5 | 401 | 421 | Liquid about 5% higher |
| 0 | 611 | 611 | Nearly equal at triple point neighborhood |
| 15 | 1705 | 1705 | Comparable magnitude when extrapolated |
How to use the calculator correctly
- Enter your target temperature in C. For this topic, set it to 15.
- Select an equation method. Murphy and Koop is the premium scientific option.
- Pick your preferred output unit: Pa, kPa, hPa, or Torr.
- Choose chart half range to control how broad the plotted temperature window is.
- Click Calculate to get numeric output, equation details, and curve visualization.
The chart helps you immediately see how sharply pressure rises with temperature. This trend is why sublimation behavior can shift fast near freezing and why accurate thermal control is critical in vacuum drying and cryogenic logistics.
Applied contexts where this number matters
- Freeze drying: chamber pressure must stay below equilibrium limits to keep sublimation active and avoid melt back.
- Cold chain storage: freezer burn risk rises when vapor pressure gradients promote moisture migration from ice rich food surfaces.
- Meteorology: deposition and sublimation in snow and cirrus systems depend on vapor pressure relative to ice equilibrium.
- Planetary science: ice stability mapping on Mars or icy moons relies on temperature pressure phase boundaries.
- HVAC and refrigeration: coil frost accumulation and defrost optimization need robust moisture phase calculations.
Accuracy, limits, and uncertainty notes
No equation is perfect in every range. For rigorous work, use a model within its validated interval and document uncertainty. The Murphy and Koop ice formula is primarily trusted in subzero conditions up to the ice melting boundary. At 15 C, treating the value as strict equilibrium over stable ice is not physically representative under ordinary pressure. It is better described as an extrapolated thermodynamic indicator.
Unit handling is another common error source. Atmospheric science often uses hPa, engineering tools often use Pa or kPa, and vacuum instruments may use Torr. The calculator converts units consistently:
- 1 kPa = 1000 Pa
- 1 hPa = 100 Pa
- 1 Torr = 133.322 Pa
If you are using the output in process design, also include chamber geometry, mass transfer coefficients, gas flow patterns, and surface temperature gradients. Equilibrium pressure alone does not predict actual sublimation rate without transport modeling.
Authoritative references for further study
For standards, property data, and atmospheric guidance, review:
- NIST Chemistry WebBook (.gov)
- NOAA scientific resources on weather and atmospheric processes (.gov)
- Penn State meteorology educational materials on vapor pressure and phase processes (.edu)
Bottom line
To calculate the sublimation pressure of ice at 15 C, use a trusted vapor pressure equation, convert units carefully, and interpret the result with thermodynamic context. The computed value is useful for analysis and comparison, but it should be labeled as extrapolative because 15 C lies above the normal stable range for bulk ice at standard pressure. For subzero engineering design, these equations are especially powerful and operationally relevant.
Practical reminder: if your real system can contain liquid water near 15 C, include water saturation pressure and phase partition effects alongside any over ice extrapolation to avoid design bias.