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Change the answer mode for this tool by selecting start temperature (T_{0}), end temperature (T_{1}), coefficient of volumetric thermal expansion (α_{V}), start volume (V_{0}) or end volume (V_{1}) as the parameter to calculate instead

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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:

T_{0} = T_{1} – (V_{1} / V_{0} – 1) / α_{V}

T_{1} = T_{0} + (V_{1} / V_{0} – 1) / α_{V}

α_{V} = (V_{1} / V_{0} – 1) / (T_{1} – T_{0})

V_{0} = V_{1} / (1 + α_{V} · (T_{1} – T_{0}))

V_{1} = V_{0} · (1 + α_{V} · (T_{1} – T_{0}))

#### Symbols

- T
_{0}= Start temperature - T
_{1}= End temperature - α
_{L}= Coefficient of volumetric thermal expansion (CVTE) - V
_{0}= Start volume - V
_{1}= End volume

### Start Temperature (T_{0})

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

### End Temperature (T_{1})

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 (V_{0})

This is the three dimensional volume of the object when it is at the start temperature T_{0} .

### End Volume (V_{1})

This is the three dimensional volume of the object following thermal expansion caused by an increase in temperature from T_{0} to T_{1} .

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