I am stuck on a physics problem which involves calculating the depth of a lake given that a bubble increases two times in volume as it rises from the bottom of a lake to the top of the lake. The problem gives the following information.

  • $T_b=5 ^\circ$
  • $T_t=25^\circ $
  • $P_\text{atm}=101325\,{\rm Pa}$
  • Lake density=$1000\,{\rm kg/m^3}$
  • $g=9.81\,{\rm m/s^2}$

Here's what I have done so far:

I have used the ideal gas equation: $$(P_1V_1)/T_1=(P_2V_2)/T_2$$

For each variable I set the following values: $P_1$ =$\rho gh+P_\text{atm}$

  • $V_1=V_i$
  • $T_1=278\,{\rm K}$
  • $P_2=P_\text{atm}$
  • $V_2=2V_i$
  • $T_2=298\,{\rm K}$

Putting all the values into the ideal gas equation, I got:

$$((\rho gh+P_\text{atm} )(V_i))/(278)=((P_\text{atm})(2V_i))/(298)$$

I modified the equation to this point and I'm stuck here. The question is asking me to find the depth of the lake, but from the looks of the equation I also need to find the volume of the bubble. I need help!


closed as off-topic by Kyle Kanos, John Rennie, stafusa, Jon Custer, sammy gerbil Aug 14 '18 at 20:20

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  • $\begingroup$ There's a pretty easy way to get rid of the $V_i$'s that should be fairly obvious. $\endgroup$ – JMac Aug 13 '18 at 12:57
  • $\begingroup$ Dividing on both sides? $\endgroup$ – AugieJavax98 Aug 13 '18 at 12:59
  • $\begingroup$ Try it yourself and see if the problem goes away? $\endgroup$ – JMac Aug 13 '18 at 13:01
  • $\begingroup$ Dividing the $V_i's$ on both sides I get $h=(Patm)(T_b)/((T_T)(\rho)(g))$ $\endgroup$ – AugieJavax98 Aug 13 '18 at 13:18
  • $\begingroup$ @AugieJavax98, it is important to stay symbolic in your work until the VERY LAST STEP. When you do this, very often, variables will "drop out" of your equation, but you will not tend to notice this if you substitute numbers into your work too early. Rework your problem, and separate "h" from the equation. THEN and only then, substitute numbers to arrive at a value. And note - properly done, you do not have to calculate the volume of the bubble. $\endgroup$ – David White Aug 13 '18 at 15:57