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Please don't ignore the template.

The space above the mercury column in a thermometer ordinarily is evacuated, but due to faulty manufacture, a particular thermometer has a pressure of 2 mmHg of air in this space when the whole thermometer is immersed in a bath at 0 degrees Celsius. Calculate the pressure of the air when the whole thermometer is immersed in a bath at 10 degrees Celsius. At 0 degrees Celsius the length of air space is 10 cm and at 10 degrees Celsius the length of air space is 2 cm.

I started out by using p = rho * g * h. For 0 degrees Celsius I got that rho = 212.31 Pa. I'm not sure that rho would be the same for 100 degrees Celsius though, because the pressure and length are changing. If rho is different, how would I go about solving for it to fill into the formula for 100 degrees celsius?

I started out by using p = rho * g * h. For 0 degrees Celsius I got that rho = 212.31 Pa. I'm not sure that rho would be the same for 100 degrees Celsius though, because the pressure and length are changing. If rho is different, how would I go about solving for it to fill into the formula for 100 degrees celsius?