I think Tim C's right to work with change in volume
a^b means a to the power of b
I've put (some) units in square brackets eg [cm]
Calculations for initial state---
CSA tube [cm^2] = pi * (0.0018^2)
Volume in tube [cm^3] = height Hg in tube * CSA_tube
Volume in bulb [cm^3] = 4/3 pi (0.25^3)
Vbefore [cm^3] = Volume_in_tube + Volume_in_bulb
(Here there's a tiny bit of an over estimation. Look very closely at the intersection of "cylinder" and sphere. It's counted twice! The "Error" caused by this, probably hardly effects the end result, and is likely to be less significant than those introduced when measuring the lengths)
Calculations for final state---
Vafter [cm^3]=Vbefore*Delta_T * coefficient V. expansion
Delta_T=35 [deg C]
Vchange = Vafter-Vbefore
Height_after[cm] = Vchange[cm^3] /CSA_tube [cm^2]
a^b means a to the power of b
I've put (some) units in square brackets eg [cm]
Calculations for initial state---
CSA tube [cm^2] = pi * (0.0018^2)
Volume in tube [cm^3] = height Hg in tube * CSA_tube
Volume in bulb [cm^3] = 4/3 pi (0.25^3)
Vbefore [cm^3] = Volume_in_tube + Volume_in_bulb
(Here there's a tiny bit of an over estimation. Look very closely at the intersection of "cylinder" and sphere. It's counted twice! The "Error" caused by this, probably hardly effects the end result, and is likely to be less significant than those introduced when measuring the lengths)
Calculations for final state---
Vafter [cm^3]=Vbefore*Delta_T * coefficient V. expansion
Delta_T=35 [deg C]
Vchange = Vafter-Vbefore
Height_after[cm] = Vchange[cm^3] /CSA_tube [cm^2]