2. An iron scale is calibrated at 0°C. The length of a
zinc rod is measured to be 100 cm by the scale when
the rod and the scale both are at 0°C. What will be
the length of the rod as measured by the scale when
both are at 100°C. Given : iron = 1.2 x 10 °C and
dezinc = 2.6 x 10-5c-
Answers
The length of the rod as measured by the scale will be 100.14 cm.
Explanation:
=> In the beginning, the rod and the scale both are at 0°C. Iron scale and rod both will expand at 100° C.
Suppose the length of zinc rod at 0 °C, Lz0 = 100 cm
αiron = 1.2 * 10⁻⁵ C⁻¹
αzink = 2.6 * 10⁻⁵ C⁻¹
=> The length of the rod as measured by the scale when both are at 100°C as it undergoes thermal expansion itself, L z t :
= L z 0 { 1 + ( αzinc − α Iron ) t }
= 100 {1 + ( 2.6 × 10 ⁻⁵ − 1.2 × 10 ⁻⁵) 100 }
= 100 {1 + ( 1.4 × 10 ⁻⁵ )10² }
= 100 { 1 + 1.4 * 10⁻³ }
= 100 {1 + 1.4/1000 }
= 100 { 1 + 0.0014}
= 100 { 1.0014 }
= 100.14 c m
Thus, the length of the rod as measured by the scale when both are at 100°C will be 100.14 cm.
Learn more:
Q:1 A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at 40°C? (Given Osteel =11x10^-6 per°C and copper = 17x10^-6 per °C)
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Q:2 A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10⁻⁵ K⁻¹.
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Explanation:
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