This wilderness essay will review historical and physics aspects of melting snow or ice to provide liquid water, a long-time problem in the freezing high-altitude environment. The simplest method of heating snow or ice is by burning firewood carried high, but when far above the tree line, mountaineers have used petroleum products, alcohols, or solid fuels in stoves with varying success and difficulties.
Many people know that at high altitude it takes more time to cook some foods because of the lower boiling point of water. Camp life and camp stove observers often recognize the results but not the why of the thermodynamics of warming snow or ice, the phase change of melting, the resultant liquid water brought to boiling at that altitude, and how this is manifests in the heating timeline. The chronicles of British explorer Eric Shipton (1907–1977) and others will be used to illustrate this facet of wilderness living at high altitude. Shipton, often with H.W. “Bill” Tilman (1898–1977), was well known for his decades of pioneering exploration and mountaineering throughout Asia. In his book Mountains of Tartary, Shipton noted that at higher camps on the mountain “producing water from snow takes at least as long as boiling the water when produced.”1(p 557) It is this basic observation, here called the “Shipton Rule,” and the physical science behind it, that is the subject of this essay.
Although most mountaineering medical topics are about hypoxia or hypothermia, and the theme of this wilderness essay might seem to be of limited practical value, it must be remembered that there are many types of challenges to living at higher altitudes. A cup of tea can rise to the occasion as paramount for hydration, warmth, and relief. During the first all-women’s Himalayan expedition in 1955, Monica Jackson affirmed, “There are times when a mug of tea assumes an importance in a climber’s life which is not to be underestimated.”2(p 178)
A simple thermodynamic model will be used to illustrate the science underlying the anecdotal observations of high-altitude explorers. A discussion of heat physics with calculations and charts will evaluate Shipton’s observation. Measuring time to melt snow or ice on the mountain, and the shorter time from there to the boiling point of water, has already been given a qualitative answer in the Shipton rule. Doing a quantitative study of his observation might be simple if it were only a single experiment in a comfortable setting at sea level. Instead, a comparison of the results at several selected high altitudes is needed.
Unfortunately, comparative measurements of gross application of heat and time to warm, melt, and boil are problematic when actually performed in the field and at different altitudes. Multiple factors and/or or assumptions for a precise answer must be controlled. The daunting list of issues includes wind; insulation; using the same type stove and pot designs and surfaces under and around them that affect conductive and convective heat losses; thermometer placement; homogenous distribution of temperature within the vessel; ambient temperature and atmospheric pressure variations from altitude, latitude, and weather systems; consistent size and character of chipped ice or scooped-up snow particles; and how many times the pot lid must be lifted to add more of either, among other variables.
Then there is the fuel itself. Shipton once complained in China, on behalf of the stove, about the “indigestible quality of the Urumchi kerosene.” 1(p 557) There are far more fuel and stove factors than this essay will evaluate—topics such as stove design and capacity, various fuel and blended fuel qualities and vaporization points, and stoichiometric consideration and efficiency that changes with altitude and temperature. Shipton points to much of the problem here: “Our primus stove ceased to function as the jets were too large for that altitude”3(p 780) Said another way, the root cause is available oxygen, or rather, available air pressure and its effect on those stove jets. As one of today’s premier winter high-altitude climbers, Simone Moro, anthropomorphized from 7700 m (25,262 ft) on Makalu, “the lack of oxygen affected not only our lungs but also the stove’s feeble flame, which seemed as tired as we were.”4(p 140)
An experimental study of gross heat application and time could be controlled with difficulty on expedition in the field, but only if done in a very meticulous, scientific way. Instead, this essay will lend credence to Shipton’s observation by calculating on paper the net energy needed to perform the tasks. At a given altitude, for constant heat output of the stove, the respective times to achieve warmed and melted snow or ice versus bringing the resultant water to boil will be proportional to net energy transferred. A clue about the results is Shipton’s choice of the word “boiling” rather than a fixed temperature.
The main factors for the calculations are temperature and high altitude, with its lower atmospheric pressure and pronounced lowering of the boiling point of water. The Table shows 5 selected heights in both metric and English measure (for historical reasons), beginning with Shipton. In July 1948, while exploring the Bogdo Ola group in Central Asia, he made one of his melting/boiling proclamations near a glacier at a campsite plagued by snow, sleet, and rain at around 3353 m (11,000 ft). As he stipulated, the Shipton rule applied to even greater heights. The next greater height in the Table is 5490 m (18,000 ft), approximating Everest base camp heights and the definition of extreme altitude.5(pp 4-5) Higher still is the Death Zone, or Todeszone, named in 1952 by Swiss physician and alpinist Edouard Wyss-Dunant.6(pp110-117) Today, it tends to get rounded off to 8000 m (26,246 ft) for the 14 highest peaks. Next is Shipton and Smythe’s Camp VI at about 8351 m (27,400 ft) on their 1933 attempt on the north slope of Everest.7(p 388) Finally, there is the Everest summit itself at 8850 m (29,035 ft), although it is uncertain that cooking has ever been performed there. Even if it has been, an attempted hard-boiled egg would only be partially so. 8
Five selected heights and physical parameters
Standard temperatures are used for calculation. These are helpful in engineering and aviation, but a mountain, as the saying goes, makes its own weather. Temperatures on the mountain may vary widely depending on local, diurnal, seasonal, latitudinal, barometric and humidity-related changes, wind, and more. Snow and ice obtained from the surface of higher glacier areas would have nighttime temperatures close to cold ambient air temperatures as opposed to daytime sun-exposed temperatures or deep subsurface ice melting from pressure. 9 The Table lists temperatures from a standard atmospheric lapse rate for use in the formulas for the model. 10 The initial temperature of the ice is assumed to be that of the standard atmospheric lapse rate temperature at the given altitude. These assigned temperatures will not fit all seasons or mountains, but a guideline must be chosen.
Altitudes and associated boiling points used for the calculations are listed in the Table. 10 Atmospheric pressure affects the boiling point of water; although there are many methods of arriving at a relationship for standard pressures versus altitude, their minor differences are ignored for the physics aspect of this essay. Deviation of the physical parameter of the boiling point of water would be so small that a change in energy or time for heating would be insignificant. For biological systems, on the other hand, low atmospheric pressure at extreme altitude accentuates what would otherwise be a small differential between a high-pressure day and a low one. Weather can sometimes produce more of a pressure fall than does a diurnal difference, seasonal swing, or deviation from a standard atmospheric model. This can raise the effective height of Everest and have a devastating physiological impact on a climber without supplemental oxygen who is at the very limit of survivability for the small fraction of people who might still be alive there in the first place.11,12
Definitions, formulas, and calculations
The formulas for the calculations are for pure snow or ice, having neither solutes nor suspended particulates nor being partially warmed by sunlight. The terms “WARM,” “MELT,” and “BOIL” will be defined as stages of heating snow or ice into boiling water that require different constants for energy inputs. 10 Energy transfers are presented as kJ/kg of ice or water.
Stage WARM is the amount of net energy required to raise snow or ice from an initial cold reading to the melting point. Snow is a form of ice with variable density, depending on compaction and history. Ice is a polycrystalline structure of water. To eliminate variable ice density in the model, a fixed mass is assumed throughout the ice and its subsequent meltwater. The net energy required to raise the temperature of a mass of ice is simply the product of the specific heat of ice times the temperature change, written as 2.1 kJ/kg°K × (rise in °K of ice from its cold initial temperature to its melting point).
Stage MELT is the amount of net energy required for the phase change of actually melting ice. Phase change is an energy-intensive transformation from one thermodynamic state to another, in this case between the solid and liquid states of water. All the energy absorbed during melting goes into breaking intermolecular forces with no rise in temperature. This is called the specific heat of fusion and requires a huge amount of energy for a mass of ice, 334 kJ/kg.
Stage MELT is constant at any altitude or pressure described here and is far larger than Stage WARM. The sum of net energy or time of combined Stage WARM + MELT is what Shipton referred to in “producing water from snow.”1(p 557)
Stage BOIL is the amount of net energy needed to raise the resultant liquid water from its freezing/melting point to its boiling point for that altitude. The net energy required to raise the temperature of a mass of water is simply the product of the specific heat of water times the temperature change, written as 4.2 kJ/kg°K × (rise in °K of water from its initial cold meltwater temperature to its incipient boiling point for that altitude). The net energy or time for BOIL is what Shipton referred to in “boiling the water when produced.”1(p 557)
These calculations yield 3 findings. First, the net energy requirement for WARM is a relatively small amount that increases with altitude and falling temperature. Second, as long as there is frozen water to start, the vast majority of the net energy needed for WARM and MELT is for the phase change of MELT. The individual proportions and large size difference in these 2 energy requirements is shown in the bar graph in Figure 1. Third, the sum of those 2 stages (WARM + MELT) is larger than the next stage of BOIL, with altitude-related changes illustrated in the line chart in Figure 2.
Bar graph shows the net energy in kJ/kg needed for stages of heating snow or ice into 0°C water at rising altitude. The black bar shows the net energy needed to raise snow or ice from low temperatures to the melting point (WARM). This is a small amount, but it increases with altitude. The white bar shows the net energy needed for phase change to convert 0°C ice to 0°C liquid water at the same temperature (MELT). This is a very large but constant amount. The sum of WARM + MELT is shown on Figure 2.
Line chart shows the net energy in kJ/kg needed for stages of heating snow or ice into boiling water at rising altitude. The upper solid line is the sum WARM + MELT, the increasing net energy needed to raise snow or ice from low temperatures to the melting point (WARM) and then convert it with phase change from frozen ice to liquid water at the same temperature (MELT). The lower dashed line is BOIL, the decreasing net energy needed to bring resultant liquid water to incipient boiling at increasingly higher altitudes and lower pressure at which the boiling point temperature falls. The divergence of the 2 lines confirms the Shipton rule that at higher altitudes WARM + MELT is greater than BOIL.
Figure 2 summarizes the Shipton rule. At successively higher and colder altitudes, additional net energy is needed for WARM because of the lower starting temperature, and although the phase change MELT stays the same as shown in Figure 1, the sum of these 2 (WARM + MELT) increases, as shown in Figure 2. In addition, a driving factor for the disparity seen in Figure 2 is the dramatically lower boiling point of water resulting from the lower pressure at increasing altitude, which reduces the amount of net energy needed for BOIL. Therefore, for temperature and pressure reasons, the net energy needed for WARM + MELT becomes increasingly larger than BOIL at higher altitudes. In Figure 2, the divergence of the 2 lines begins just above the altitude at which Shipton made his proclamation about what happens at even greater heights, an area with which he was exceedingly familiar.
Mountaineering history and physics
Some practical comments and physics will be discussed from the perspective of high-altitude mountaineering history. The issues of time and energy with underpowered or bulky equipment, uncertain fuels, the lower boiling point of water, and slow-to-prepare foodstuffs were important in past years and remain so today.
Hydration is an immediate requirement, but where there is no liquid water up high, obtaining the preferred hottest version of water can be an agonizingly slow process. In the 1930s on the north side of Everest, Shipton gave up on his underpowered stove and used little tins of solid fuel called Tommy Cookers. He found that these “were inefficient at that height, and it took an hour to provide two miserable cups of tepid water.”7(p 389) By the 1980s on Everest in winter, cooking and drinking was still no easy chore, with Joe Tasker similarly wisecracking that “making another cup of tea was an event as important as a dinner party, and took about as long to prepare.”13(p 130)
Early physician-mountaineers like TG Longstaff (1875–1964) and RWG Hingston (1887–1966) wrote briefly about the problem of dehydration.14(p 46),15(p 252) However, it was physiologist Griffith Pugh (1909–1994) who was the first to fully emphasize that enough liquid intake was necessary, even life-saving, for success at extreme altitude. Pugh, on Cho Oyo in 1952 and Everest in 1953, stressed hydration, and even improved the slow stove design to help the cause. Edmund Hillary grudgingly admitted that Pugh was right to push fluids. He and Tenzing brewed volumes of liquids, enough that the New Zealander felt the need to relieve himself on the summit.16(pp 12,44,92,143,194,195)
At high altitude, there are many food and food-related issues such as lack of acclimatization, loss of appetite, palatability, digestibility, insufficient provisions, gastrointestinal illnesses, and water temperature. With long marches to the Greater Ranges, early high-altitude pioneers took large stores of food and fuel and supplies, often having hundreds of porters carry heavy loads in siege-style assaults. Shipton and Tilman, the models of the alternative lightweight approach, famously wrote that they could plan an expedition simply on the back of an envelope. Both climbers were prolific and articulate authors. Tilman specialized in wry observations and said about food that “at greater heights eating it becomes more a duty than a pleasure.”17(p 206) Others agreed with that sentiment. British climber and wit Frank Smythe was with Shipton in 1933 and half-joked that “there is something peculiarly unappetizing about a frozen sardine in gelatinous oil at 25,700 feet [7833 meters].”18(p 602)
The physics seen in the Shipton rule has a practical impact on obtaining hot food as well as hot water by itself. This was exemplified in reports from Tibet in 1903–1904 by British Medical Officer and Indian Army surgeon Laurence Austine Waddell (1854–1938). He complained that high-altitude cooking caused “indigestion… chiefly from insufficient fuel, and the lowered boiling point of water… insufficient to burst the starch grains of rice.” 19 On Everest in 1933, Shipton remarked on mealtime preparation by saying that “melting a saucepan full of snow for water and bringing it to boil took so long that people tended to delude themselves that they had eaten a hearty meal.”7(p384) Even with today’s better stoves and food preservation, thin brews of packet soup may still have orange and green bits that fail to rehydrate, and instant pastas may not soften well with the lower boiling point of water. Pressure cookers have occasionally been used so that their hotter water might better soften certain fare.
Shipton used the same old battered Primus stove for 2 decades to boil water and cook food, but he also came to an accurate conclusion about cooking his hypsometer while at 4267 m (14,000 ft) on Chakragil in Central Asia. Before accurate topographic maps and global positioning systems, mountaineers estimated their altitude with this device, which heated a thermometer. A depressed boiling point of water indicated lower air pressure and thus inversely the height of the mountain. Shipton, ever looking to reduce carried weight, noted that “while supper was cooking, we boiled our hypsometer. We discovered that, not unnaturally, the thermometer gave the same reading when immersed in boiling tea-water as in the ingenious little steam-engine provided by the makers, so we decided to lighten our loads by the weight of the latter.”1(p 581)
Altitude and temperature are important in calculations. Ordinarily, it is cold at altitude. The lapse-rate–derived calculations here estimate a harsh scenario with a summit temperature below –40°C and cold temperatures more like winter on Everest. This adds to the WARM part of the equation, but even at milder temperatures, the Shipton rule still applies. As long as there is snow or ice to start, the huge energy needs of phase change (MELT) dominate WARM + MELT. For example, climbing season on Everest is usually late spring, but despite an average Everest summit temperature in October of –25°C, an unusually warm day of –9°C was recorded in 1981. 11 Even if there were ice with a temperature of exactly 0°C at the top of Everest, say during the summer monsoon when it is not usually climbed, the Shipton rule would still be true. In that 0°C situation, the only heat required for WARM + MELT would be the large energy requirement for phase change alone (ie, MELT). At such a relatively mild temperature, the drop in boiling point at extreme altitude would be the only factor that keeps WARM + MELT > BOIL to satisfy the Shipton rule.
The only exception to Shipton’s conclusion high on the mountain is with the use of heavy pressure cookers, but these are typically used only at basecamps. The extra heat needed for boiling at a higher pressure and higher temperature in a pressure cooker would change the results. Other than in this scenario, and by the method in this essay of calculating net heat energy needed for WARM + MELT vs BOIL, the observation of Himalayan mountaineer Eric Shipton is confirmed.
In their own ways and times, mountaineers learned about living in conditions of cold and thin air. The mountaineering accounts included in this essay help to relate a unique and evocative story, both in terms of wilderness literature and as illustrations of some of the physics of high altitude. The corroboration was performed by calculating net energy needed to perform the tasks of warming ice, melting it, and bringing the resultant water to boil. Alternately, studying gross energy and time could be performed in a meticulous, controlled, scientific way on expedition. Others are invited to take up this challenge to validate these conclusions on the mountain.
Footnotes
Acknowledgment:
The author thanks Remi Sojka, who helped watch water boil at 5944 m.