# What Is the Dimensional Formula of Coefficient of Thermal Expansion

The length variation ΔL is proportional to the length L. The dependence of thermal expansion on temperature, substance and length is summarized in the equation ΔL = αLΔT, where ΔL is the change in length L, ΔT is the change in temperature and α is the coefficient of linear expansion that varies slightly with temperature. This difference in extent can also lead to problems with the interpretation of the fuel gauge. The actual amount (mass) of gasoline that remains in the tank when the indicator is „empty“ is much lower in summer than in winter. Gasoline has the same volume as in winter, when the light comes on „add fuel“,“ but because gasoline has expanded, there is less mass. If you`re used to still having 40 „empty“ miles in the winter, be careful – you`ll probably get out much faster in the summer. The forces and pressures generated by thermal stresses are generally as large as in the example above. Railways and roads can deform in hot weather if they lack expansion joints. (See Figure 5.) Power lines collapse more in summer than in winter and break down in cold weather when there is not enough room for manoeuvre. Cracks open and close in plaster walls when a house warms up and cools. Glass pans crack when cooled quickly or unevenly due to differential contraction and the stresses it creates. (Pyrex® is less sensitive due to its low coefficient of thermal expansion.) Pressure vessels in nuclear reactors are at risk of cooling too quickly and, although none have failed, some have cooled faster than was considered desirable.

Biological cells are torn when food is frozen, which affects their taste. Repeated thawing and freezing increases the damage. The oceans can also be affected. A significant part of the sea level rise resulting from global warming is due to the thermal expansion of seawater. Table 1 lists representative values of the linear expansion coefficient, which can have units of 1/ºC or 1/K. Since the size of a Kelvin and a degree Celsius is the same, α and ΔT can be expressed in units of Kelvin or degrees Celsius. The equation ΔL = αLΔT is accurate for small temperature changes and can be used for large temperature changes when an average value of α is used. Use the linear thermal expansion equation ΔL = αLΔT to calculate the length change, ΔL.

Use the linear expansion coefficient α for steel in Table 1 and note that the temperature change ΔT is 55ºC. Figure 1. Thermal expansion joints like this one in the Auckland Harbour Bridge in New Zealand allow bridges to change length without buckling. (Photo credit: Ingolfson, Wikimedia Commons) Two blocks, A and B, are made of the same material. Block A has dimensions l × w × h = L × 2L × L and block B has dimensions 2L × 2L × 2L. If the temperature changes, which is not large compared to the length of the bridge, but this change in length is observable. It is usually distributed over many expansion joints, so the expansion at each joint is small. The tank and gasoline increase in volume, but gasoline increases further, so the amount spilled is the difference in their volume changes. (The gas tank can be treated like solid steel.) We can use the volume expansion equation to calculate the change in volume of gasoline and tank.

Another example of heat stress can be found in the mouth. Dental fillings can expand differently than tooth enamel. It can cause pain when you eat ice cream or drink a hot drink. Cracks may appear in the filling. Metal fillings (gold, silver, etc.) are replaced by composite fillings (porcelain), which have lower coefficients of expansion and are close to those of teeth. For small temperature changes, the change in the ΔA zone is given by ΔA = 2αAΔT, where ΔA is the change in zone A, ΔT is the temperature change, and α is the linear coefficient of expansion that varies slightly with temperature. linear expansion coefficient: α, the change in length, per unit length, by temperature change of 1 ° C; a constant used in the calculation of the linear extent; The coefficient of linear expansion depends on the material, and to some extent the temperature of the material, this amount is important, especially for a tank of 60.0 liters. .

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