The gas law was applied in celsius

# Self-authored for the EML case corpus (no external origin). An operator watches
# the absolute pressure gauge on a sealed gas vessel climb from 200 kPa at 20
# degrees Celsius to 300 kPa. Knowing that the pressure of a sealed gas is
# proportional to its temperature, the operator reasons that pressure up by half
# means temperature up by half - from 20 to 30 degrees, warm but safe. The gas
# really reached a temperature computed below.
#
# The reasoning is careful. The gauge reads absolute pressure and is accurate;
# the vessel really is sealed, so the amount of gas and its volume are fixed;
# for such a gas pressure really is proportional to temperature; and the intent
# is exactly 'how hot is the gas'.
#
# The proportion holds only for temperature counted from absolute zero, 273.15
# degrees below the Celsius zero. 20 degrees Celsius is 293.15 on that scale;
# half as much again is 439.72, which is 166.57 degrees Celsius. The gas is 136
# degrees hotter than the operator believes.

200 => pressure_before_kpa
300 => pressure_now_kpa
2000 => temperature_before_hundredths_c
27315 => zero_celsius_above_absolute_zero_hundredths

int(temperature_before_hundredths_c / 100) => temperature_before_c
int(temperature_before_hundredths_c * pressure_now_kpa / pressure_before_kpa) => temperature_now_by_celsius_ratio_hundredths_c
temperature_before_hundredths_c + zero_celsius_above_absolute_zero_hundredths => temperature_before_hundredths_k
int(temperature_before_hundredths_k * pressure_now_kpa / pressure_before_kpa) => temperature_now_hundredths_k
temperature_now_hundredths_k - zero_celsius_above_absolute_zero_hundredths => temperature_now_hundredths_c
int(temperature_now_by_celsius_ratio_hundredths_c / 100) => temperature_believed_c
int(temperature_now_hundredths_c / 100) => temperature_actual_c
temperature_actual_c - temperature_believed_c => hotter_than_believed_by_c
int((pressure_now_kpa - pressure_before_kpa) * 100 / pressure_before_kpa) => pressure_rise_percent

"pressure                        : " + str(pressure_before_kpa) + " kPa, now " + str(pressure_now_kpa) + " kPa, up " + str(pressure_rise_percent) + " percent" ^0
"temperature before              : " + str(temperature_before_hundredths_c) + " hundredths of a degree C" ^0
"celsius zero above absolute zero : " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree" ^0
"" ^0
"now, by a celsius ratio         : " + str(temperature_now_by_celsius_ratio_hundredths_c) + " hundredths of a degree C" ^0
"before, from absolute zero      : " + str(temperature_before_hundredths_k) + " hundredths of a kelvin" ^0
"now, from absolute zero         : " + str(temperature_now_hundredths_k) + " hundredths of a kelvin" ^0
"now, in celsius                 : " + str(temperature_now_hundredths_c) + " hundredths of a degree C" ^0
"" ^0
"believed                        : " + str(temperature_believed_c) + " C" ^0
"actual                          : " + str(temperature_actual_c) + " C" ^0
"hotter than believed by         : " + str(hotter_than_believed_by_c) + " degrees" ^0
"" ^0

# ---- what the operator verified ----

"the up-by-half reasoning" ^0
"  gauge : absolute pressure, accurate" ^0
"  vessel : sealed, so the gas and its volume are fixed" ^0
"  law : pressure proportional to temperature" ^0
"  intent : how hot is the gas" ^0
"  facts wrong : 0" ^0
"  verdict : THE GAS IS AT " + str(temperature_believed_c) + " DEGREES, WARM BUT SAFE" ^0
"" ^0
"  reading an absolute gauge on a sealed vessel is the part done" ^0
"  right here, and it is why the pressure ratio of " + str(pressure_now_kpa) + " to " + str(pressure_before_kpa) ^0
"  really does equal the temperature ratio" ^0
"" ^0

# ---- where the proportion starts ----

"a ratio needs a true zero" ^0
"  what the law is proportional to : temperature counted from" ^0
"    absolute zero, where a gas would press on nothing" ^0
"  where celsius starts : " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree above that" ^0
"  " + str(temperature_before_hundredths_c) + " hundredths of a degree C : " + str(temperature_before_hundredths_k) + " from absolute zero" ^0
"  up by half : " + str(temperature_now_hundredths_k) + ", which is " + str(temperature_now_hundredths_c) + " hundredths of a degree C" ^0
"  what the celsius ratio did : scaled the distance from an ice" ^0
"    point that the gas knows nothing about" ^0
"" ^0

# ---- what the operator got ----

"the vessel" ^0
"  believed : " + str(temperature_believed_c) + " C" ^0
"  actual : " + str(temperature_actual_c) + " C" ^0
"  is the gas law wrong : no; the pressure did rise with the" ^0
"    temperature, exactly in proportion" ^0
"  is celsius a scale you can take ratios on : no; its zero is" ^0
"    a convention, not an absence" ^0
"" ^0

# ---- null control ----

# The same reading converted through the absolute scale instead of scaled in
# celsius.
30 => nc_temperature_read_with_a_celsius_ratio_c
166 => nc_temperature_read_with_an_absolute_ratio_c
136 => nc_degrees_the_true_zero_adds

"null control - take the ratio from absolute zero" ^0
"  temperature, read with a celsius ratio : " + str(nc_temperature_read_with_a_celsius_ratio_c) + " C" ^0
"  temperature, read with an absolute ratio : " + str(nc_temperature_read_with_an_absolute_ratio_c) + " C" ^0
"  degrees the true zero adds : " + str(nc_degrees_the_true_zero_adds) ^0
"  no gauge and no gas changed; the proportion was applied to the" ^0
"  quantity it is a proportion of" ^0
"" ^0

# ---- the rule ----

"what an accurate gauge and the gas law guarantee" ^0
"  the temperature rose in proportion to the pressure : exactly" ^0
"  the gas went from " + str(temperature_before_c) + " to " + str(temperature_believed_c) + " degrees C : not addressed; the" ^0
"    proportion runs from absolute zero, and " + str(temperature_before_hundredths_k) + " hundredths of" ^0
"    a kelvin up by half is " + str(temperature_actual_c) + " degrees C, " + str(hotter_than_believed_by_c) + " hotter than believed" ^0
"" ^0

"a ratio is only as honest as the zero it is counted from; move the zero and" ^0
"half as much again becomes a different half" ^0
"" ^0

"The pressure rose by half and the temperature did too - on the absolute scale." ^0
"In celsius the vessel went from " + str(temperature_before_c) + " to " + str(temperature_actual_c) + " degrees, not to " + str(temperature_believed_c) + ", because" ^0
"the proportion is counted from absolute zero, " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree below" ^0
"the celsius zero, until the ratio is taken on the scale the law is written in." ^0

pressure_before_kpa = 200
pressure_now_kpa = 300
temperature_before_hundredths_c = 2000
zero_celsius_above_absolute_zero_hundredths = 27315
temperature_before_c = int(temperature_before_hundredths_c / 100)
temperature_now_by_celsius_ratio_hundredths_c = int(temperature_before_hundredths_c * pressure_now_kpa / pressure_before_kpa)
temperature_before_hundredths_k = temperature_before_hundredths_c + zero_celsius_above_absolute_zero_hundredths
temperature_now_hundredths_k = int(temperature_before_hundredths_k * pressure_now_kpa / pressure_before_kpa)
temperature_now_hundredths_c = temperature_now_hundredths_k - zero_celsius_above_absolute_zero_hundredths
temperature_believed_c = int(temperature_now_by_celsius_ratio_hundredths_c / 100)
temperature_actual_c = int(temperature_now_hundredths_c / 100)
hotter_than_believed_by_c = temperature_actual_c - temperature_believed_c
pressure_rise_percent = int((pressure_now_kpa - pressure_before_kpa) * 100 / pressure_before_kpa)
print("pressure                        : " + str(pressure_before_kpa) + " kPa, now " + str(pressure_now_kpa) + " kPa, up " + str(pressure_rise_percent) + " percent")
print("temperature before              : " + str(temperature_before_hundredths_c) + " hundredths of a degree C")
print("celsius zero above absolute zero : " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree")
print("")
print("now, by a celsius ratio         : " + str(temperature_now_by_celsius_ratio_hundredths_c) + " hundredths of a degree C")
print("before, from absolute zero      : " + str(temperature_before_hundredths_k) + " hundredths of a kelvin")
print("now, from absolute zero         : " + str(temperature_now_hundredths_k) + " hundredths of a kelvin")
print("now, in celsius                 : " + str(temperature_now_hundredths_c) + " hundredths of a degree C")
print("")
print("believed                        : " + str(temperature_believed_c) + " C")
print("actual                          : " + str(temperature_actual_c) + " C")
print("hotter than believed by         : " + str(hotter_than_believed_by_c) + " degrees")
print("")
print("the up-by-half reasoning")
print("  gauge : absolute pressure, accurate")
print("  vessel : sealed, so the gas and its volume are fixed")
print("  law : pressure proportional to temperature")
print("  intent : how hot is the gas")
print("  facts wrong : 0")
print("  verdict : THE GAS IS AT " + str(temperature_believed_c) + " DEGREES, WARM BUT SAFE")
print("")
print("  reading an absolute gauge on a sealed vessel is the part done")
print("  right here, and it is why the pressure ratio of " + str(pressure_now_kpa) + " to " + str(pressure_before_kpa))
print("  really does equal the temperature ratio")
print("")
print("a ratio needs a true zero")
print("  what the law is proportional to : temperature counted from")
print("    absolute zero, where a gas would press on nothing")
print("  where celsius starts : " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree above that")
print("  " + str(temperature_before_hundredths_c) + " hundredths of a degree C : " + str(temperature_before_hundredths_k) + " from absolute zero")
print("  up by half : " + str(temperature_now_hundredths_k) + ", which is " + str(temperature_now_hundredths_c) + " hundredths of a degree C")
print("  what the celsius ratio did : scaled the distance from an ice")
print("    point that the gas knows nothing about")
print("")
print("the vessel")
print("  believed : " + str(temperature_believed_c) + " C")
print("  actual : " + str(temperature_actual_c) + " C")
print("  is the gas law wrong : no; the pressure did rise with the")
print("    temperature, exactly in proportion")
print("  is celsius a scale you can take ratios on : no; its zero is")
print("    a convention, not an absence")
print("")
nc_temperature_read_with_a_celsius_ratio_c = 30
nc_temperature_read_with_an_absolute_ratio_c = 166
nc_degrees_the_true_zero_adds = 136
print("null control - take the ratio from absolute zero")
print("  temperature, read with a celsius ratio : " + str(nc_temperature_read_with_a_celsius_ratio_c) + " C")
print("  temperature, read with an absolute ratio : " + str(nc_temperature_read_with_an_absolute_ratio_c) + " C")
print("  degrees the true zero adds : " + str(nc_degrees_the_true_zero_adds))
print("  no gauge and no gas changed; the proportion was applied to the")
print("  quantity it is a proportion of")
print("")
print("what an accurate gauge and the gas law guarantee")
print("  the temperature rose in proportion to the pressure : exactly")
print("  the gas went from " + str(temperature_before_c) + " to " + str(temperature_believed_c) + " degrees C : not addressed; the")
print("    proportion runs from absolute zero, and " + str(temperature_before_hundredths_k) + " hundredths of")
print("    a kelvin up by half is " + str(temperature_actual_c) + " degrees C, " + str(hotter_than_believed_by_c) + " hotter than believed")
print("")
print("a ratio is only as honest as the zero it is counted from; move the zero and")
print("half as much again becomes a different half")
print("")
print("The pressure rose by half and the temperature did too - on the absolute scale.")
print("In celsius the vessel went from " + str(temperature_before_c) + " to " + str(temperature_actual_c) + " degrees, not to " + str(temperature_believed_c) + ", because")
print("the proportion is counted from absolute zero, " + str(zero_celsius_above_absolute_zero_hundredths) + " hundredths of a degree below")
print("the celsius zero, until the ratio is taken on the scale the law is written in.")

pressure                        : 200 kPa, now 300 kPa, up 50 percent
temperature before              : 2000 hundredths of a degree C
celsius zero above absolute zero : 27315 hundredths of a degree

now, by a celsius ratio         : 3000 hundredths of a degree C
before, from absolute zero      : 29315 hundredths of a kelvin
now, from absolute zero         : 43972 hundredths of a kelvin
now, in celsius                 : 16657 hundredths of a degree C

believed                        : 30 C
actual                          : 166 C
hotter than believed by         : 136 degrees

the up-by-half reasoning
  gauge : absolute pressure, accurate
  vessel : sealed, so the gas and its volume are fixed
  law : pressure proportional to temperature
  intent : how hot is the gas
  facts wrong : 0
  verdict : THE GAS IS AT 30 DEGREES, WARM BUT SAFE

  reading an absolute gauge on a sealed vessel is the part done
  right here, and it is why the pressure ratio of 300 to 200
  really does equal the temperature ratio

a ratio needs a true zero
  what the law is proportional to : temperature counted from
    absolute zero, where a gas would press on nothing
  where celsius starts : 27315 hundredths of a degree above that
  2000 hundredths of a degree C : 29315 from absolute zero
  up by half : 43972, which is 16657 hundredths of a degree C
  what the celsius ratio did : scaled the distance from an ice
    point that the gas knows nothing about

the vessel
  believed : 30 C
  actual : 166 C
  is the gas law wrong : no; the pressure did rise with the
    temperature, exactly in proportion
  is celsius a scale you can take ratios on : no; its zero is
    a convention, not an absence

null control - take the ratio from absolute zero
  temperature, read with a celsius ratio : 30 C
  temperature, read with an absolute ratio : 166 C
  degrees the true zero adds : 136
  no gauge and no gas changed; the proportion was applied to the
  quantity it is a proportion of

what an accurate gauge and the gas law guarantee
  the temperature rose in proportion to the pressure : exactly
  the gas went from 20 to 30 degrees C : not addressed; the
    proportion runs from absolute zero, and 29315 hundredths of
    a kelvin up by half is 166 degrees C, 136 hotter than believed

a ratio is only as honest as the zero it is counted from; move the zero and
half as much again becomes a different half

The pressure rose by half and the temperature did too - on the absolute scale.
In celsius the vessel went from 20 to 166 degrees, not to 30, because
the proportion is counted from absolute zero, 27315 hundredths of a degree below
the celsius zero, until the ratio is taken on the scale the law is written in.

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