Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is ?2.0°C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C? (b) If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is 33.0°C?

Solution 25E Original length L = 12.0 m 0 0 Change in temperature T = 33 C ( 2 ) C 0 T = 35 C Coefficient of linear expansion of steel is = 12 × 106/ C (a) Therefore, the change in length L = LT 6 0 0 L = 12 × 10 / C × 12.0 m × 35 C 6 L = 5040 × 10 m L = 0.005 m L = 5.0 × 10 3 m 3 Therefore, the space that has to be left is 5.0 × 10m. (b) We know , Stress = Y steel × T Stress = 2.0 × 10 11 N/m × 12 × 10 6/ C × 35 C0 5 2 Stress = 840 × 10 N/m 7 Stress = 8.40 × 10 Pa Therefore, the stress in them is 8.40 × 10 Pa.