Volumetric Thermal Expansion Calculator

Calculate Volumetric Thermal Expansion Parameters
Select Answer Mode	T0 T1 αV V0 V1
Start Temperature (T0) [?]
⟳ Select temperature unit degrees Celsius (°C) degrees Fahrenheit (°F) kelvins (K) degrees Rankine (°R) quectokelvins (qK) rontokelvins (rK) yoctokelvins (yK) zeptokelvins (zK) attokelvins (aK) femtokelvins (fK) picokelvins (pK) nanokelvins (nK) microkelvins (µK) millikelvins (mK) centikelvins (cK) decikelvins (dK) kelvins (K) decakelvins (daK) hectokelvins (hK) kilokelvins (kK) megakelvins (MK) gigakelvins (GK) terakelvins (TK) petakelvins (PK) exakelvins (EK) zettakelvins (ZK) yottakelvins (YK) ronnakelvins (RK) quettakelvins (QK)
End Temperature (T1) [?]
⟳ Select temperature unit degrees Celsius (°C) degrees Fahrenheit (°F) kelvins (K) degrees Rankine (°R) quectokelvins (qK) rontokelvins (rK) yoctokelvins (yK) zeptokelvins (zK) attokelvins (aK) femtokelvins (fK) picokelvins (pK) nanokelvins (nK) microkelvins (µK) millikelvins (mK) centikelvins (cK) decikelvins (dK) kelvins (K) decakelvins (daK) hectokelvins (hK) kilokelvins (kK) megakelvins (MK) gigakelvins (GK) terakelvins (TK) petakelvins (PK) exakelvins (EK) zettakelvins (ZK) yottakelvins (YK) ronnakelvins (RK) quettakelvins (QK)
CVTE (αV) [?]
Select CVTE unit per degree Celsius (/°C) per degree Fahrenheit (/°F) per kelvin (/K) per degree Rankine (/°R) ppm per degree Celsius (ppm/°C) ppm per degree Fahrenheit (ppm/°F) ppm per kelvin (ppm/K) ppm per degree Rankine (ppm/°R) per quectokelvin (/qK) per rontokelvin (/rK) per yoctokelvin (/yK) per zeptokelvin (/zK) per attokelvin (/aK) per femtokelvin (/fK) per picokelvin (/pK) per nanokelvin (/nK) per microkelvin (/µK) per millikelvin (/mK) per centikelvin (/cK) per decikelvin (/dK) per kelvin (/K) per decakelvin (/daK) per hectokelvin (/hK) per kilokelvin (/kK) per megakelvin (/MK) per gigakelvin (/GK) per terakelvin (/TK) per petakelvin (/PK) per exakelvin (/EK) per zettakelvin (/ZK) per yottakelvin (/YK) per ronnakelvin (/RK) per quettakelvin (/QK) ppm per quectokelvin (ppm/qK) ppm per rontokelvin (ppm/rK) ppm per yoctokelvin (ppm/yK) ppm per zeptokelvin (ppm/zK) ppm per attokelvin (ppm/aK) ppm per femtokelvin (ppm/fK) ppm per picokelvin (ppm/pK) ppm per nanokelvin (ppm/nK) ppm per microkelvin (ppm/µK) ppm per millikelvin (ppm/mK) ppm per centikelvin (ppm/cK) ppm per decikelvin (ppm/dK) ppm per kelvin (ppm/K) ppm per decakelvin (ppm/daK) ppm per hectokelvin (ppm/hK) ppm per kilokelvin (ppm/kK) ppm per megakelvin (ppm/MK) ppm per gigakelvin (ppm/GK) ppm per terakelvin (ppm/TK) ppm per petakelvin (ppm/PK) ppm per exakelvin (ppm/EK) ppm per zettakelvin (ppm/ZK) ppm per yottakelvin (ppm/YK) ppm per ronnakelvin (ppm/RK) ppm per quettakelvin (ppm/QK)
Start Volume (V0) [?]
⟳ Select volumetric unit cu centimetres (cc, cm³) millilitres (mL) teaspoons (tsp, metric) teaspoons (tsp, usa) cu inches (in³) fluid ounces (fl oz, imp) fluid ounces (fl oz, usa) pints (pt, usa liq) pints (pt, imp) litres (L) gallons (gal, usa liq) gallons (gal, imp) cu feet (ft³) cu metres (m³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cc, cm³) millilitres (mL) teaspoons (tsp, metric) tablespoons (Tbsp, metric) cups (metric) litres (L) cu metres (m³) kilolitres (kL) megalitres (ML) cu kilometres (km³) cu thous (thou³) cu inches (in³) fluid ounces (fl oz, imp) pints (pt, imp) gallons (gal, imp) cu feet (ft³) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) cu thous (thou³) teaspoons (tsp, usa) tablespoons (Tbsp, usa) cu inches (in³) fluid ounces (fl oz, usa) cups (usa) pints (pt, usa liq) gallons (gal, usa liq) cu feet (ft³) barrels (bbl, oil) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) quectolitres (qL) rontolitres (rL) yoctolitres (yL) zeptolitres (zL) attolitres (aL) femtolitres (fL) picolitres (pL) nanolitres (nL) microlitres (µL) millilitres (mL) centilitres (cL) decilitres (dL) litres (L) decalitres (daL) hectolitres (hL) kilolitres (kL) megalitres (ML) gigalitres (GL) teralitres (TL) petalitres (PL) exalitres (EL) zettalitres (ZL) yottalitres (YL) ronnalitres (RL) quettalitres (QL) cu quectometres (qm³) cu rontometres (rm³) cu yoctometres (ym³) cu zeptometres (zm³) cu attometres (am³) cu femtometres (fm³) cu picometres (pm³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cm³) cu decimetres (dm³) cu metres (m³) cu decametres (dam³) cu hectometres (hm³) cu kilometres (km³) cu megametres (Mm³) cu gigametres (Gm³) cu terametres (Tm³) cu petametres (Pm³) cu exametres (Em³) cu zettametres (Zm³) cu yottametres (Ym³) cu ronnametres (Rm³) cu quettametres (Qm³) cu astronomical units (au³) cu light-years (ly³) cu parsecs (pc³) cu kiloparsecs (kpc³) cu megaparsecs (Mpc³) cu gigaparsecs (Gpc³)
End Volume (V1) [?]
⟳ Select volumetric unit cu centimetres (cc, cm³) millilitres (mL) teaspoons (tsp, metric) teaspoons (tsp, usa) cu inches (in³) fluid ounces (fl oz, imp) fluid ounces (fl oz, usa) pints (pt, usa liq) pints (pt, imp) litres (L) gallons (gal, usa liq) gallons (gal, imp) cu feet (ft³) cu metres (m³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cc, cm³) millilitres (mL) teaspoons (tsp, metric) tablespoons (Tbsp, metric) cups (metric) litres (L) cu metres (m³) kilolitres (kL) megalitres (ML) cu kilometres (km³) cu thous (thou³) cu inches (in³) fluid ounces (fl oz, imp) pints (pt, imp) gallons (gal, imp) cu feet (ft³) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) cu thous (thou³) teaspoons (tsp, usa) tablespoons (Tbsp, usa) cu inches (in³) fluid ounces (fl oz, usa) cups (usa) pints (pt, usa liq) gallons (gal, usa liq) cu feet (ft³) barrels (bbl, oil) cu yards (yd³) cu miles (mi³) cu nautical miles (nmi³) quectolitres (qL) rontolitres (rL) yoctolitres (yL) zeptolitres (zL) attolitres (aL) femtolitres (fL) picolitres (pL) nanolitres (nL) microlitres (µL) millilitres (mL) centilitres (cL) decilitres (dL) litres (L) decalitres (daL) hectolitres (hL) kilolitres (kL) megalitres (ML) gigalitres (GL) teralitres (TL) petalitres (PL) exalitres (EL) zettalitres (ZL) yottalitres (YL) ronnalitres (RL) quettalitres (QL) cu quectometres (qm³) cu rontometres (rm³) cu yoctometres (ym³) cu zeptometres (zm³) cu attometres (am³) cu femtometres (fm³) cu picometres (pm³) cu nanometres (nm³) cu micrometres (µm³) cu millimetres (mm³) cu centimetres (cm³) cu decimetres (dm³) cu metres (m³) cu decametres (dam³) cu hectometres (hm³) cu kilometres (km³) cu megametres (Mm³) cu gigametres (Gm³) cu terametres (Tm³) cu petametres (Pm³) cu exametres (Em³) cu zettametres (Zm³) cu yottametres (Ym³) cu ronnametres (Rm³) cu quettametres (Qm³) cu astronomical units (au³) cu light-years (ly³) cu parsecs (pc³) cu kiloparsecs (kpc³) cu megaparsecs (Mpc³) cu gigaparsecs (Gpc³)

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User Guide

This tool will calculate any parameter from the formula V₁=V₀(1+αᵥ(T₁-T₀)) for volumetric thermal expansion, which includes the start temperature, end temperature, coefficient of volumetric thermal expansion (CVTE), start volume and end volume.

The volumetric thermal expansion formula is used to calculate the change in volume of a three dimensional object, due to a change in temperature. The precision of volumetric expansion is very good if the change in volume is small compared to the overall volume of the of the object, and the thermal coefficient of expansion of the material does not change by much, within the range of temperature change.

Formulas

The formulas used by this volumetric thermal expansion calculator to determine each individual parameter are:

T₀ = T₁ – (V₁ / V₀ – 1) / α_V

T₁ = T₀ + (V₁ / V₀ – 1) / α_V

α_V = (V₁ / V₀ – 1) / (T₁ – T₀)

V₀ = V₁ / (1 + α_V · (T₁ – T₀))

V₁ = V₀ · (1 + α_V · (T₁ – T₀))

Symbols

• T₀ = Start temperature
• T₁ = End temperature
• α_L = Coefficient of volumetric thermal expansion (CVTE)
• V₀ = Start volume
• V₁ = End volume

Start Temperature (T₀)

This is the temperature of the object before the temperature is increased.

End Temperature (T₁)

This is the temperature of the object after the temperature has been increased

Coefficient Of Volumetric Thermal Expansion (CVTE, α_V)

This is a fixed value which is used to determine how much a small change in temperature will affect the three dimensional volume of a particular substance. The coefficient defines the fractional change in volume of a substance per unit change in its temperature.

Start Volume (V₀)

This is the three dimensional volume of the object when it is at the start temperature T₀ .

End Volume (V₁)

This is the three dimensional volume of the object following thermal expansion caused by an increase in temperature from T₀ to T₁ .