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castrodisastro
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Homework Statement
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.
Homework Equations
ε=1-(T2/T1)
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