What is the correct solution for the temperature expansion problem?

[bolzano95]

Homework Statement

A steel container is filled with alcohol. For how much kelvins we have to raise the temperature for the pressure to be raised by 6 bar?
Compressibility of alcohol is
<br /> \kappa=1.15 \cdot 10^{-4} bar^{-1}<br />
temperature coefficient of volume expansion of alcohol is
<br /> \beta_a= 7.5 \cdot 10^{-4} K^{-1}<br />
temperature coefficient of length expansion of steel is
<br /> \alpha_s= 1.2 \cdot 10^{-5} K^{-1}<br />

Homework Equations

Look at attempt at solution.

The Attempt at a Solution

I solved this problem like this:
<br /> \frac{\Delta V}{V}=(\beta_a-3\alpha)\Delta T\\<br /> \frac{\Delta V}{V}=\kappa\Delta p\\<br /> \frac{\kappa\Delta p}{\beta_a-3\alpha}=\Delta T= 0.97K\\<br />
But the solution is wrong. The correct answer is 9.7K. I'm interested where I made a mistake.

 

[kuruman]

It looks like your answer is off by a factor of 10. This may be due to a typo or an error in the conversion of compressibility units to bar^-1.

 

[bolzano95]

I checked and get 0.97K. Do you think the solving process is correct?

 

[kuruman]

The method is correct. If you are certain that the input numbers are also correct, then the answer in the back of the book may be a typo.