Thermodynamics - Ideal Gas Model

  1. I've been working on this problem for a couple of hours, and I can't seem to crack it. I feel like just a tip on how to get started would get me up over the hump.

    1. The problem statement, all variables and given/known data

    Two pistons in two different cylinders are connected by a rigid rod. A pin used to fix the pistons in place is removed and the system is allowed to equilibrate adiabatically. Assuming that air behaves as an ideal gas, determine the temperature of the gas in Tank A and Tank B (Tf) at the final state assuming that the temperatures are equal.

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    2. Relevant equations

    Pv=RT

    3. The attempt at a solution

    I attempted to find the volume of each of the chambers in the initial state by using Pv = RT at both the top and bottom chamber.

    I came up with v_top=.01435 m^3 and v_bottom=.010045 m^3

    I'm unsure where to go from here. I know that P_1*v_1=mRT_1 and P_2*v_2=mRT_2. I'm just unsure how to relate all of this to finding the final temperature.
     
  2. jcsd
  3. Do you know what kind of gas it is? The relationships of P,V,T,etc. for adiabatic processes are typically dependent on the number of degrees of freedom the gas has.

    If not, then there should be a way to derive it using only the ideal gas law. Here are some relationships that may help you out, if you solve everything for R, you can set the equations for the four states equal to each other. Let me know if these get you anywhere.

    PV=RT => PV/T=R

    (P_ai)(V_ai)/(T_ai)=R
    (P_af)(V_af)/(T_f)=R
    (P_bi)(V_bi)/(T_bi)=R
    (P_bf)(V_bf)/(T_f)=R

    (P_ai)(V_ai)/(T_ai)=(P_af)(V_af)/(T_f)=(P_bi)(V_bi)/(T_bi)=(P_bf)(V_bf)/(T_f)=R

    (T_f)=[(P_af)(V_af)]/[(P_ai)(V_ai)/(T_ai)]=[(P_bf)(V_bf)]/[(P_bi)(V_bi)/(T_bi)]
    (T_f)=[(P_af)(V_af)(T_ai)]/[(P_ai)(V_ai)]=[(P_bf)(V_bf)(T_bi)]/[(P_bi)(V_bi)]
     
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