Work and Heat Flow of a Heat Engine Cycle

Also, the work should be positive since the engine is doing work.W = (-3.00 atm)(0.600 m^3)(101325 Pa/1 atm) = -18195 J = 1.82 kJb)The heat flow into the engine per cycle can be calculated by finding the area under the curve on the PV diagram. This can be done by breaking the cycle into two parts: isothermal expansion and isobaric compression.Isothermal Expansion:Q = nRTln(V2/V1)Q = (1 mol)(8.31 J/molK)(300 K)ln(1.200 m^3/0.600 m^3) = 1.79 kJIs
  • #1
ally1h
61
0

Homework Statement


A heat engine follows the cycle shown in the figure. a) How much net work is done by the engine in one cycle? b) what is the heat flow into the engine per cycle?

Diagram:
http://farm4.static.flickr.com/3050/2703330973_26acb35c27.jpg?v=0



Homework Equations


W = -PΔV
ΔU = Q+W



The Attempt at a Solution


a)
W = -PΔV
W = (-3.00 atm)(0.600 m^3)
W = -1.8 J

b)
ΔU = Q+W
ΔU = 0, due to energy conservation
so...
0 = Q+W
Q = W
Q = 1.8




Everything look okay? I wasn't so sure about part b...
 
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  • #2
Probably in part (b) the question asks for total heat added to the engine per one cycle, not the net heat gained (i.e. not [added]-[removed]). So, you should decide which part of the cycle corresponds to heating and then use

[tex]dQ = p\, dV + V\, dp[/tex]

to calculate the heat.
 
  • #3
ally1h said:

The Attempt at a Solution


a)
W = -PΔV
W = (-3.00 atm)(0.600 m^3)
W = -1.8 J

Your pressure needs to be converted into Pa to get the right units.
 

Related to Work and Heat Flow of a Heat Engine Cycle

1. What is a heat engine cycle?

A heat engine cycle is a thermodynamic process in which heat energy is converted into mechanical work. It typically involves the cyclic transfer of heat between a hot reservoir and a cold reservoir, with the work output occurring during the expansion phase of the cycle.

2. How does a heat engine cycle work?

A heat engine cycle works by utilizing the first and second laws of thermodynamics. The first law states that energy cannot be created or destroyed, only transferred or converted. The second law states that heat will naturally flow from a hot object to a cold object. By harnessing this heat flow and converting it into work, a heat engine can operate.

3. What is the difference between work and heat in a heat engine cycle?

In a heat engine cycle, work refers to the energy that is produced by the engine and can be used to perform tasks. Heat, on the other hand, is the transfer of thermal energy between objects. In a heat engine cycle, heat is used to produce work, and any remaining heat is released to the environment.

4. What factors affect the efficiency of a heat engine cycle?

The efficiency of a heat engine cycle is affected by several factors, including the temperature difference between the hot and cold reservoirs, the type of working fluid used, and the design and efficiency of the engine itself. Generally, a larger temperature difference and a more efficient engine will result in a higher efficiency.

5. Why is the Carnot cycle considered the most efficient heat engine cycle?

The Carnot cycle is considered the most efficient heat engine cycle because it is a theoretical model that operates at the maximum possible efficiency for a given temperature difference. This is due to the fact that it operates reversibly, meaning there is no energy lost during the heat transfer process. However, in practical applications, the efficiency of a Carnot cycle is not achievable due to various limitations.

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