Photo AI

Which is a correct statement about an ideal heat engine? Tick (✓) one box - AQA - A-Level Physics - Question 5 - 2021 - Paper 6

Question icon

Question 5

Which-is-a-correct-statement-about-an-ideal-heat-engine?--Tick-(✓)-one-box-AQA-A-Level Physics-Question 5-2021-Paper 6.png

Which is a correct statement about an ideal heat engine? Tick (✓) one box. The efficiency is increased when the kelvin temperatures of the hot source and the cold ... show full transcript

Worked Solution & Example Answer:Which is a correct statement about an ideal heat engine? Tick (✓) one box - AQA - A-Level Physics - Question 5 - 2021 - Paper 6

Step 1

The efficiency is 50% when the kelvin temperature of the hot source is twice the kelvin temperature of the cold sink.

96%

114 rated

Answer

This statement is correct according to the efficiency equation for an ideal heat engine given by:

extEfficiency=1−TcTh ext{Efficiency} = 1 - \frac{T_c}{T_h}

If the hot source temperature ThT_h is twice the cold sink temperature TcT_c, then: Th=2TcT_h = 2T_c Substituting this into the efficiency equation gives: extEfficiency=1−Tc2Tc=1−12=0.5extor50% ext{Efficiency} = 1 - \frac{T_c}{2T_c} = 1 - \frac{1}{2} = 0.5 ext{ or } 50\%

Step 2

Determine the coefficient of performance COP_ref of the refrigerator.

99%

104 rated

Answer

The coefficient of performance for a refrigerator, COP_ref, is defined as:

COPref=QhWCOP_{ref} = \frac{Q_h}{W}

We know: W=Qh−QcW = Q_h - Q_c

For an ideal engine efficiency given as 0.330.33: η=WQh=0.33\eta = \frac{W}{Q_h} = 0.33

Therefore, substituting for work: W=0.33QhW = 0.33 Q_h

Now rearranging gives: Qc=Qh−W=Qh−0.33Qh=0.67QhQ_c = Q_h - W = Q_h - 0.33 Q_h = 0.67 Q_h

Substituting this back into the COP formula yields: COPref=Qh0.33Qh=10.33≈3.03COP_{ref} = \frac{Q_h}{0.33 Q_h} = \frac{1}{0.33} \approx 3.03

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;