Calculating Temperature Change from 20°C to -20°C: Homework Question

[chetzread]

Homework Statement

in this question , it's not stated that whether the temperature change from 20°C to -20°C or -20°C to 20°C .
I'm confused...

Homework Equations

The Attempt at a Solution

I think it should be changing from 20°C to -20°C so delta T = (-20-20) = -40°C , am i right ?

 

[drvrm]

I think it should be changing from 20°C to -20°C so delta T = (-20-20) = -40°C , am i right ?

the limiting stress is given at -20 degree so if you use it one will have to go to that temp. therefore the temp change is of 40 degrees.

 

[chetzread]

the limiting stress is given at -20 degree so if you use it one will have to go to that temp. therefore the temp change is of 40 degrees.

do you mean the temperature goes from -20 to 20 ? if so , the temperature change is -40°C , am i right ?

 

[drvrm]

do you mean the temperature goes from -20 to 20 ? if so , the temperature change is -40°C , am i right ?

The rod was kept at 20 degrees and from there it has been moved to -20 degrees so the change in temperature is in two parts +20 to zero and zero to -20 degrees so the total change is of 40 degrees (change in temperature is a number the negative and positive signs of a temp. only shows its position on a scale...

.in both the parts of the above change the stress is increasing and going to add up to the limit... given .

If you wish to say it that change is -40 degrees and put the negative sign in your relation for the limiting stress one will make an error as it will denote a reduction...which may not be the the physical situation!

 

[Chestermiller]

Yes, you are right, the temperature change is -40 degrees. Would that tend to make the rod shorter if it were free to contract? So, to keep the rod the same length, would the stress in the rod have to increase or decrease?

 

[chetzread]

Yes, you are right, the temperature change is -40 degrees. Would that tend to make the rod shorter if it were free to contract? So, to keep the rod the same length, would the stress in the rod have to increase or decrease?

The rod shorter if it were free to contract , stress in the rod have to increase to keep the rod same length

 

[Chestermiller]

So, from our famous equation $\sigma=E(\epsilon-\alpha \Delta T)$, if $\epsilon = 5000/(AE)$ and $\Delta T = -40$, what do you get for $\sigma.$?

 

[chetzread]

So, from our famous equation $\sigma=E(\epsilon-\alpha \Delta T)$, if $\epsilon = 5000/(AE)$ and $\Delta T = -40$, what do you get for $\sigma.$?

ok , solved

 

[chetzread]

So, from our famous equation $\sigma=E(\epsilon-\alpha \Delta T)$, if $\epsilon = 5000/(AE)$ and $\Delta T = -40$, what do you get for $\sigma.$?

i don't really understand , how could the εs = positive ?
the εs = strain ?
so , the steel rod contract , εs = negative ?

 

[Chestermiller]

i don't really understand , how could the εs = positive ?
the εs = strain ?
so , the steel rod contract , εs = negative ?

The steel rod was stretched initially and then, when it was cooled, it was not allowed to contract. So its strain remained positive.