Thermodynamics; Tension due to Temperature?

Question

A stainless steel band (coefficient of linear expansion = 17.3 10-6°C-1; Young's modulus = 18 1010 N/m2) is placed around a tooth. It is essentially circular with an initial mean radius of 5.0 mm, a height of 3.6 mm, and a thickness of 0.46 mm. If the band just fits snugly over the tooth when heated to a temperature of 77°C, what is the tension in the band when it cools to a temperature of 37°C?
????N

Answer 1

The relaxed length decreases by a factor dL/L = 17.3E-6*40.
Stress S = 18E10 * dL/L
Tension = strap area * S = 200.54 N
(Strap area = 0.0035*0.00046)