Carnot cycle, heat and monatomic ideal gas

In summary, the conversation discussed the use of a monatomic ideal gas in a Carnot cycle, with specific isothermal and adiabatic processes. The question posed was how much heat is expelled by the gas during one of the adiabatic processes, given that 400 J of work was done by the gas during another process. The answer was determined to be less than 400 J, with one participant using the efficiency of the Carnot cycle and another using the adiabatic equation to arrive at their respective solutions.
  • #1
frznfire219
7
0
Hi, I would appreciate any help with this:

A monatomic ideal gas is used as the working substance for
the Carnot cycle. Processes A => B and C => D
are isothermal, while processes B => C and D => A are adiabatic.
During process A => B, there are 400 J of work done by the gas on
the surroundings. How much heat is expelled by the gas during process C => D?

So I'm completely stuck, all I know is that it's less than 400 J, obviously.
There's a picture of the corresponding PV graph actually at http://www.compadre.org/psrc/evals/Physics_Bowl_2003.pdf (page 12).

Thanks for any help!
 
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  • #2
anyone?
 
  • #3
I'm not sure about this explanation, but whatever. You know that the carnot cycle runs at perfect efficiency ie. 1-(Ql/Qh) and you know that efficiency of the carnot cycle is also 1-(Tl/Th). I get 100 J.
 
  • #4
Thanks! I actually figured it out later with the adiabatic equation (PV^gamma is constant) but your way is much more elegant.
 

FAQ: Carnot cycle, heat and monatomic ideal gas

What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. It is often used as a benchmark for the maximum possible efficiency of a heat engine.

How does the Carnot cycle demonstrate the relationship between heat and work?

In the Carnot cycle, heat is converted into work through the expansion and compression of a gas. The isothermal processes involve the transfer of heat into or out of the gas, while the adiabatic processes involve the gas performing work without any heat exchange.

What is an ideal gas in relation to the Carnot cycle?

An ideal gas is a theoretical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of the gas are related by the equation PV = nRT. In the Carnot cycle, an ideal gas is used to simplify the calculations and demonstrate the principles of thermodynamics.

Can the Carnot cycle be applied to all types of gases?

Yes, the Carnot cycle can be applied to any gas, as long as it follows the ideal gas law. However, for more complex gases, the calculations may become more complicated and the ideal gas assumption may not hold true.

What is the efficiency of a Carnot cycle?

The efficiency of a Carnot cycle is given by the equation e = 1 - (Tlow/Thigh), where Tlow is the temperature at the end of the isothermal expansion process and Thigh is the temperature at the end of the isothermal compression process. This means that the efficiency of a Carnot cycle is determined solely by the temperatures at which heat is added and rejected.

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