Questions: Problem 2: (9% of Assignment Value) In this problem a heat engine, each cycle, absorbs an amount of energy Qh=1780 J from a hot reservoir and expels an amount Qc=1310 J into a cold reservoir. Each cycle lasts for a time of t=0.23 seconds. Part (a) Find the efficiency of an ideal engine operating between these reservoirs. Remember the efficiency is unit-less, therefore so should your number be. eideal =

Problem 2: (9% of Assignment Value) In this problem a heat engine, each cycle, absorbs an amount of energy Qh=1780 J from a hot reservoir and expels an amount Qc=1310 J into a cold reservoir. Each cycle lasts for a time of t=0.23 seconds. Part (a) Find the efficiency of an ideal engine operating between these reservoirs. Remember the efficiency is unit-less, therefore so should your number be. eideal =
Transcript text: Problem 2: (9\% of Assignment Value) In this problem a heat engine, each cycle, absorbs an amount of energy $Q_{h}=1780 \mathrm{~J}$ from a hot reservoir and expels an amount $Q_{c}=1310 \mathrm{~J}$ into a cold reservoir. Each cycle lasts for a time of $t=0.23$ seconds. Part (a) Find the efficiency of an ideal engine operating between these reservoirs. Remember the efficiency is unit-less, therefore so should your number be as well. \[ e_{\text {ideal }}=\square \]
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given a heat engine that absorbs energy \( Q_h = 1780 \, \text{J} \) from a hot reservoir and expels energy \( Q_c = 1310 \, \text{J} \) to a cold reservoir. We need to find the efficiency of this engine.

Step 2: Recall the Formula for Efficiency

The efficiency \( e \) of a heat engine is given by the formula: \[ e = \frac{W}{Q_h} \] where \( W \) is the work done by the engine. The work done can be calculated as the difference between the heat absorbed and the heat expelled: \[ W = Q_h - Q_c \]

Step 3: Calculate the Work Done

Substitute the given values into the formula for work: \[ W = 1780 \, \text{J} - 1310 \, \text{J} = 470 \, \text{J} \]

Step 4: Calculate the Efficiency

Now, substitute the values of \( W \) and \( Q_h \) into the efficiency formula: \[ e = \frac{470 \, \text{J}}{1780 \, \text{J}} \]

Step 5: Simplify the Efficiency Expression

Calculate the efficiency: \[ e = \frac{470}{1780} \approx 0.2640 \]

Final Answer

The efficiency of the engine is \(\boxed{0.2640}\).

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