1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Heat Efficiency of a Carnot Engine

  1. Feb 6, 2014 #1
    1. The problem statement, all variables and given/known data
    A Carnot engine operates between a warmer reservoir at a temperature T1 and a cooler reservoir at a temperature T2. It is found that increasing the temperature of the warmer reservoir by a factor of 2.00 while keeping the same temperature for the cooler reservoir increases the efficiency of the Carnot engine by a factor of 5.00. Find the efficiency of the engine and the ratio of the temperatures of the two reservoirs in their original form.


    2. Relevant equations
    ε=1-(T2/T1)


    3. The attempt at a solution

    I think we are supposed to get a numerical value for an answer but I don't think I have enough information.

    So I start with

    ε=1-(T2/T1)

    The question states, "increasing the temperature of the warmer reservoir by a factor of 2.00 while keeping the same temperature for the cooler reservoir increases the efficiency of the Carnot engine by a factor of 5.00"

    That means T1 will be doubled and once that happens, ε is quintupled, resulting in...

    5ε=1-(T2/2T1)

    The question asks for the efficiency, which I am supposed to answer with a numerical value. So I tried solving for ε.

    ε=(1/5)-(T2/10T1))

    I can't think of a way to solve this with 2 independent variables. Am I ignoring something from the question that would point me towards a value? Maybe I'm forgetting some mathematical property?

    Once I have the efficiency then I can solve for the ratio of the two temperatures. Since it asks me for the ratio, I assume that knowing T1 and T2 are not required, so how could we solve for ε and get a numerical value?

    Thanks in advance
     
  2. jcsd
  3. Feb 6, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Use R for ##T_1/T_2##. Now you have 2 equations in 2 unknowns!
     
  4. Feb 6, 2014 #3
    Thanks! I knew it was staring at me in the face.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Heat Efficiency of a Carnot Engine
Loading...