Thermal Stress (Thermodynamics)

[Luongo]

1. Equation F/A=-Y$$\alpha$$$$\Delta$$T (thermal stress) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount $$\Delta$$L when its temperature changes by $$\Delta$$T, the stress is equal to F/A = Y(($$\Delta$$L/L$$_{}0$$)-$$\alpha\Delta$$T) where F is the tension on the rod, L(naut) is the original length of the rod, A its cross-sectional area, alpha its coefficient of linear expansion, and Y its Young's modulus.


i don't know where to start can somebody help? this thermal stress is stressing me out

 

[Luongo]

please help any feedback I am begging you

 

[Andrew Mason]

1. Equation F/A=-Y$$\alpha$$$$\Delta$$T (thermal stress) gives the stress required to keep the length of a rod constant as its temperature changes. Show that if the length is permitted to change by an amount $$\Delta$$L when its temperature changes by $$\Delta$$T, the stress is equal to F/A = Y(($$\Delta$$L/L$$_{}0$$)-$$\alpha\Delta$$T) where F is the tension on the rod, L(naut) is the original length of the rod, A its cross-sectional area, alpha its coefficient of linear expansion, and Y its Young's modulus.


i don't know where to start can somebody help? this thermal stress is stressing me out

If the length changes by dL what does the volume change by? So what does the area, A, change by? How does this affect the stress, F/A?

AM

 

[Luongo]

If the length changes by dL what does the volume change by? So what does the area, A, change by? How does this affect the stress, F/A?

AM

if the length changes the area would increase and the pressure would decrease. I'm not sure how you "Show This" though