engine / thermo question?

Question

The ideal gas in a Carnot engine extracts 1000 J of heat energy during the isothermal expansion at 300C.
How much heat energy is exhausted during the isothermal compression at 50C?

Answer 1

Ok, I am considering "C" as celsius, but if is not correct, I will do it donwards considering "C" as Kelvin, anyway :

The ideal gas in a Carnot engine, has an efficiency, that can be calculated as :

n = 1 - T2 / T1

T1 = 300 + 273 = 573 K

T2 = 50 + 273 = 323 K

n = 1 - 323 / 573 = 0.44 >>> 44 %

Let's call the heat extracted as : Q1 J

and the heat exhausted as : Q2 J

And, the efficiency can be calculated also as :

n = Q1 - Q2 / Q1

0.44 = 1000 - Q2 / 1000

Q2 = 560 (joules)

Just remeber the formulas, now if "C" is kelvin :

n = 1 - 50 / 300 = 0.83

n = 1000 - Q2 / 1000 = 0.83

Q2 = 170 joules

Anyway, I think "C" is celsius, so you have both procedures, hope that helped, and remeber this topic is not difficult, is very interesting and useful.