- #1

castrodisastro

- 82

- 0

## Homework Statement

A Carnot engine operates between a warmer reservoir at a temperature

**and a cooler reservoir at a temperature**

*T*_{1}**. It is found that increasing the temperature of the warmer reservoir by a factor of**

*T*_{2}**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-(**)

*T*_{2}/*T*_{1}## 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-(**

*T*_{2}/*T*_{1})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

**will be doubled and once that happens,**

*T*_{1}**ε**is quintupled, resulting in...

**5ε=1-(**

*T*_{2}/2*T*_{1})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)-(**

*T*_{2}/10*T*_{1}))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

**and**

*T*_{1}**are not required, so how could we solve for**

*T*_{2}**ε**and get a numerical value?

Thanks in advance