Hello,

I am working on a problem from "elements of classical thermodynamics" by A.B.Pippard (Q10, pg.161) as following,

According to experimental measurements, alpha iron transforms into gamma iron at 906 degree Celcius and back to alpha iron at 1400 degree Celcius. Between these temperatures the specific heat of gamma iron rises linearly from 0.160 cal g^{−1}deg^{−1}. to 0.169 cal g^{−1}deg^{−1}. On the assumption that alpha iron, if it were stable between 906 and 1400 degree Celcius, would have a specific heat constant at the value 0.185 cal g^{−1}deg^{−1} that it has at both these temperatures, estimate the latent heat at each transition temperature.

I tried this as following and do not think it was right. Any help or suggestion is greatly appreciated!

Let :delta: h_{1} be latent heat at the transition from alpha iron into gamma iron at 906 degree Celcius

:delta: h_{2} be latent heat at the transition from gamma iron into alpha iron at 1400 degree Celcius

the internal heat change for alpha iron per gram , if it were stable between 906 and 1400 degree Celcius, would be

:delta: U=0.185*(1400-906)=97.76cal.g^{-1}

the internal heat change for gamma iron per gram from 906 and 1400 degree Celcius is

/int_906^1400(.160+0.009/(1400-906)(T-906))dT=89.72 cal.g^{-1}

So we have :delta: h_{1} + :delta: h_{2}= 91.76-89.72cal.g^{-1}=2.04cal.g^{-1} (1)

And :delta: h=dp/dT*T :delta: v

apply it to both transitions, since :delta: v_{1}=- :delta: v_{2} and dp/dT=const (do not know why?), We have

:delta: h_{1}/ :delta: h_{2}=-T_{1}/T_{2}=-906/1400 (2)

solve (1) and (2), we have

:delta: h_{1}=-3.74cal.g^{-1}

:delta: h_{2}=5.78cal.g^{-1}

It is probably not right, can any of you help me out?

If I am luckily right, can you tell me why we have dp/dT=const same for both transitions