Heat Cycle

Practice Problems
Heat Cycle

Directions: On this worksheet all questions are based on this PV diagram. 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 48 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 = 33ºC and the temperature at position B is T₂ = 652ºC.

How many moles of helium are present in the container?

3 moles7.22 x 10²⁴ moles1.99 x 10^-26 moles12 moles

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

AB and CDCD and DAAB and BCBC and DA

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Question 3 If P₁ equals 190 kPa, then what is the value of P₂?

574 kPa313 kPa463 kPa283 kPa

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

2.48 x 10^-1 m³6.43 x 10² m³1.73 x 10^-2 m³1.61 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?

372.0 K1224.0 K405.0 K918.0 K

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

the correct value
is not given8.74 x 10¹ J7.97 x 10^-7 J1.69 x 10^-20 J1.4 x 10^-19 J

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

AB and CDBC and DAAB and BCCD and DA

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

3.7 x 10³ J4.15 x 10⁵ J5.54 x 10⁵ J2.77 x 10⁵ J

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

0 J -2.77 x 10⁵ J -1.85 x 10⁵ J -9.16 x 10⁴ J

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

5.54 x 10⁵ J 4.3 x 10⁵ J the correct value
is not given6.18 x 10⁴ J 6.15 x 10⁵ J

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

91.7 % 24.4 % 8.3 % 75.0 %

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

30.1 % 61.6 % 69.9 % 43.1 %