Thermal Physics

fasterthanjoao

this is my second set of questions today, revising for an exam just now. would be grateful to anyone that can answer

1) The pendulum of a clock consists of a thin steel rod carrying a small heavy bob. the clock keeps correct time at 15 degrees centigrade, calculate the error in twenty four hours if the temperature rises to an average value of 20 degrees C.

coefficient of linear thermal expansion of steel = 11x10^-6

2) The reading of a true barometer and one containing a little air are 760mm and 700mm. when the air is partly exhausted from the space surrounding them they read 380mm and 360mm. Find the height from the mercury level in the reservoir to the top of the faulty tube.


thanks again, hopefully I won't have to post any-more problems later

cepheid

1. I hope that this question is asking you to find the error in the next twenty-four hours after the temperature reaches 20 degrees. Because if it is asking you to find the error as the temperature rises to 20 degress over the course of twenty-four hours, then that sounds much more difficult to me.

Let's assume the former scenario is what was intended. So, what happens to the steel when the temperature rises? It will expand, and you know exactly by how much. You've been given the coefficient of thermal expansion, which, if I remember right, tells you how much the length of the rod changes, as a fraction of the original length, per degree Celsius.

So, knowing by how much the length increases, what can you say about the period of oscillation of the pendulum? How does the length of a pendulum affect its period (what equation shows the relationship explicitly)? How will the change in period affect its timekeeping? From that, you can calculate the error that will accumulate in 24 hrs.