A Carnot engine is set up to produce a certain work W per cycle. In each cycle, energy in the form of heat QHis transferred to the working substance of the engine from the higher-temperature thermal reservoir, which is at an adjustable temperature TH. The lower-temperature thermal reservoir is maintained at temperature TL=250K. Figure 20-58 gives QH for a range of TH . The scale of the vertical axis is set by QHs=6.0KJ. If THis set at 550 K , what is QH?

Short Answer

Expert verified

The value of heat QHis 1692 J .

Step by step solution

01

The given data

Lower temperature isTL=250K

The heat that the scale is set atQHs=6KJ

Higher temperature is TH=550K

02

Understanding the concept of the Carnot cycle

We use the relation between work, higher and lower temperature, and heat to find the work done from the initial values given, and then we can find the value of the required heat.

Formula:

The efficiency of the engine gives the given relation of heat, work, and temperature,

WQH=(TH-Tc)TH (1)

03

Calculation of heat, 

The work done using equation (1) and taking any values from the graph for QHsand TH can be given as:

W4000J=(325K-250K)325KW=923J

Again using the same equation, we can findQHfrom the new high temperatureTH',

WQH=(TH'-TC)TH'923JQH=(550K-250K)550K923JQH=0.5454QH=923J0.5454=1692J

We used the relation for work, higher and lower temperature, and heat to find QH.

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