Heat Cycle

PhysicsLAB

Practice Problems
Heat Cycle

Topics: On this worksheet all questions are based on the PV diagram shown below.

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The y-axis represents pressure measured in kPa while the x-axis represents volume measured in cubic meters. The enclosed gas used throughout this problem is Helium, a monatomic gas which has a specific heat for constant volume of C_V = 3/2R; and a specific heat for constant pressure of C_P = 5/2R.

PV diagram

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Question 1 40 grams of gas follow the process AB, BC, CD, and DA as shown above. You are given that the temperature at position A is T₁ = 30ºC and the temperature at position B is T₂ = 658ºC.

How many moles of helium are present in the container?

1.66 x 10^-26 moles6.02 x 10²⁴ moles10 moles2.5 moles

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Question 2 In which processes was heat removed from the gas?

BC and DAAB and CDCD and DAAB and BC

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Question 3 If P₁ equals 180 kPa, then what is the value of P₂?

281 kPa395 kPa453 kPa553 kPa

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Question 4 What is the value of V₁, the original volume of the container?

1.4 x 10^-1 m³5.6 x 10² m³1.39 x 10^-2 m³1.98 x 10^-1 m³

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Question 5 If during this heat cycle the volume of the gas expands to a maximum value of V₂ = 4V₁, what is the temperature at position D?

393.0 K1212.0 K363.0 K909.0 K

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Question 6 What is the average translational kinetic energy of a gas molecule at poisiton D?

8.69 x 10^-7 J8.69 x 10¹ J1.67 x 10^-20 J1.39 x 10^-19 J the correct value
is not given

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Question 7 In which processes was no work done on or by the gas?

AB and CDCD and DABC and DAAB and BC

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Question 8 By how much does the internal energy of the gas increase during process BC?

3.72 x 10³ J3.48 x 10⁵ J2.32 x 10⁵ J4.64 x 10⁵ J

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Question 9 What is the net work done on the gas during this heat cycle?

-7.56 x 10⁴ J -1.57 x 10⁵ J 0 J -2.32 x 10⁵ J

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Question 10 How much heat is added during one complete cycle?

4.64 x 10⁵ J 5.17 x 10⁵ J 5.22 x 10⁴ J 3.6 x 10⁵ J the correct value
is not given

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Question 11 What is the ideal Carnot efficiency for this heat cycle?

8.1 % 91.9 % 23.2 % 75.0 %

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Question 12 What is the actual efficient of this heat cycle?

61.5 % 30.3 % 69.7 % 43.5 %

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