To calculate the difference in length of the steel bridge between a 30°C day in August and a -10°C night in January, we need to consider the coefficient of thermal expansion for steel. The coefficient of thermal expansion for steel is approximately 0.000012 per degree Celsius.First, we calculate the expansion for the 30°C day in August:
Expansion = Length x Coefficient x Change in Temperature
Expansion = 300m x 0.000012 x (30°C - 0°C)
Expansion = 300m x 0.000012 x 30°C
Expansion = 0.108m or 10.8 cmNext, we calculate the contraction for the -10°C night in January:
Contraction = Length x Coefficient x Change in Temperature
Contraction = 300m x 0.000012 x (-10°C - 0°C)
Contraction = 300m x 0.000012 x -10°C
Contraction = -0.036m or -3.6 cmThe difference in length between the two temperatures is the sum of the expansion and contraction:
Difference = Expansion + Contraction
Difference = 0.108m + (-0.036m)
Difference = 0.072m or 7.2 cmTherefore, the steel bridge will be approximately 7.2 cm longer on a 30°C day in August than on a -10°C night in January.