Calculating Work Done by a Carnot Engine

[Darth Geek]

Homework Statement

An ideal Carnot engine takes in 160 kcal of heat at 110°C and exhausts some of this at 10°C. How much work (in joules) must have been done by the engine?

Homework Equations

The engine's efficiency is ε = (T_H - T_L)/T_H.

The hint tells me that I need to use the First Law of Thermodynamics to calculate the work, which is

∆U = Q - W.

I also have the equation

ε = |W|/|Q_T|.

The Attempt at a Solution

The efficiency is (383.15 - 283.15) / 383.15 = 0.261

but how do I find Q_T? I converted the 160 Cal. to Joules and got 669888 J... but somehow that seems like a lot- is it right?

 

[aniketp]

but how do I find Q_T? I converted the 160 Cal. to Joules and got 669888 J... but somehow that seems like a lot- is it right?

Its a carnot engine consisting of 2 adiabatic and 2 isothermal lines.
Use this to find Q_T

 

[Darth Geek]

So, I just sum up the work done by each of the processes?

Sorry, but Apex (Not-)Learning doesn't say much on the subject. I may be able to sift through the cruft that they call notes to see how to do this, though.

 

[Darth Geek]

Sorry for the double post but I don't see an "edit" button...

How do I find the work for each individual process? All I have to go on is the 160 kcal.

 

[stewartcs]

Sorry for the double post but I don't see an "edit" button...

How do I find the work for each individual process? All I have to go on is the 160 kcal.

The thermal efficiency of a heat engine is given by:

$$\eta_{th} = \frac{W_{net,out}}{Q_{in}}$$

Since it is a Carnot engine you can use the temperatures of the reseviors to determine the efficiency (but you already knew this since you have the efficiency correct).

Solve for the work since they give you the heat input.

CS

 

[Darth Geek]

I got the question right. Thanks everyone. :)