Thermodynamics_worksheet-key

Molar Mass & Avogadro’s Number:

1. Determine the atomic mass for the following elements: {from the textbook}

a) hydrogen (H):  1.00797 g/mol

b) argon (Ar):  39.948 g/mol

c) carbon (C):  12.01115 g/mol

d) oxygen (O):  15.9994 g/mol

2. Determine the molecular mass for the following compounds:

a) oxygen gas (O₂):  31.9988 g/mol

b) carbon dioxide (CO₂):  44.00995 g/mol

c) methane (CH₄):  16.4303 g/mol

3.  Determine the molar quantity of the following:

a) 0.10 kg of Ar: 2.5 mol

b) 0.010 kg of O₂: 3.1 mol

c) 0.15 kg of CO₂: 3.4 mol

d) 1.0 kg methane (CH₄): 62.3 mol

4.  Determine the number of molecules for the following:

a) 0.10 kg of Ar: 1.5x10²⁴ atoms

b) 0.010 kg of O₂: 1.9x10²⁴ molecules

c) 0.15 kg of CO₂: 2.1x10²⁴ molecules

d) 1.0 kg methane (CH₄): 3.8x10²⁵ molecules

5. A sample of monatomic ideal gas is originally at 20°C.  What is the final temperature of the gas if both the pressure and volume are doubled?

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6. Heat is absorbed by a sample of a monatomic ideal gas at 40 °C.  It is observed that the gas expands until its volume is doubled and the pressure drops to half of its original value.  What is the final temperature of the gas?

Ans.

7. A canister containing 150 kg of an ideal gas has a volume of 8.0 m³. If the gas exerts a pressure of 5.0 ´ 10⁵ Pa, what is the rms speed of the molecules?

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8. A tank contains 135 moles of the monatomic gas, argon, at a temperature of 15.3 °C.  How much energy must be added to the gas to increase its temperature to 45.0 °C?

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9. An ideal gas with a fixed number of molecules is maintained at a constant pressure.  At 30.0 °C, the volume of the gas is 1.50 m³. What is the volume of the gas when the temperature is increased to 75.0 °C?

Ans. 

Constant Temperature (Isothermal) Processes:

1.  A sample of 10.0 moles of a monatomic ideal gas, held at constant temperature (1000K), is expanded from 0.10 m³ to 0.20 m³.

a. What is the initial pressure of the gas, before heating?

Ans. 

b. What is the initial internal energy of the gas?

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c. How much work is performed by the gas during the heating process?

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d. What is the final internal energy of the gas?

Ans. Since DT=0 K,

e. What is the change in internal energy of the gas?

Ans. E_int=0 J

f. Conceptually, is heat absorbed or released by the gas during the compression?

Ans.  Q is absorbed since the gas does work but E_int doesn’t change.

g. Calculate the amount of heat absorbed/released by the gas?

Ans.    or

Constant Pressure (Isobaric) Processes:

2.  A sample of 10.0 moles of a monatomic ideal gas, held at constant pressure (1.5 atm or 1.52x10⁵ Pa), is compressed from 0.10 m³ to 0.05 m³.

a. What is the initial temperature of the gas, before the compression?

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b. What is the initial internal energy of the gas?

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c. How much work is performed by the gas during the compression?

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d. What is the final temperature of the gas?

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e. What is the change in internal energy of the gas?

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f. Conceptually, is heat absorbed or released by the gas during the compression? 

Ans.  Both E_int and W have increased; this requires that Q be absorbed to account for the additional energy.

g. Calculate the amount of heat absorbed/released by the gas?

Ans. 

3.  A sample of 5.0 moles of a monatomic ideal gas, held at constant pressure (2.0 atm or 2.026x10⁵ Pa), is expanded from 0.05 m³ to 0.10 m³.

a. What is the initial temperature of the gas, before the compression?

Ans. 

b. What is the initial internal energy of the gas?

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c. How much work is performed by the gas during the compression?

Ans. 

d. What is the final temperature of the gas?

Ans. 

e. What is the change in internal energy of the gas?

Ans. 

f. Conceptually, is heat absorbed or released by the gas during the compression?

Ans.  Both E_int and W have increased; this requires that Q be absorbed to account for the additional energy.

g. Calculate the amount of heat absorbed/released by the gas?

Ans. 

Constant Volume (Isochoric) Processes:

4.  A sample of 10.0 moles of a monatomic ideal gas, held at constant volume (1.0 m³), is heated from 300 K to 400 K.

a. What is the initial pressure of the gas, before heating?

Ans. 

b. What is the initial internal energy of the gas?

Ans. 

c. How much work is performed on the gas during the heating process?

Ans.  W = 0 J

d. What is the final internal energy of the gas?

Ans. 

e. What is the change in internal energy of the gas?

Ans. 

f. Conceptually, is heat absorbed or released by the gas during the compression?

Ans. Since E_int increases, Q must be absorbed to account for the additional energy.

g. Calculate the amount of heat absorbed/released by the gas?

Ans. 

4.  A sample of 10.0 moles of a diatomic ideal gas, held at constant volume (1.0 m³), is heated from 250 K to 400 K.

a. What is the initial pressure of the gas, before heating?

Ans. 

b. What is the initial internal energy of the gas?

Ans. 

c. How much work is performed on the gas during the heating process?

Ans.  W = 0 J

d. What is the final internal energy of the gas?

Ans. 

e. What is the change in internal energy of the gas?

Ans. 

f. Conceptually, is heat absorbed or released by the gas during the compression?

Ans. Since E_int increases, Q must be absorbed to account for the additional energy.

g. Calculate the amount of heat absorbed/released by the gas?

Ans. 

Adiabatic Processes:

5.  A sample of 1.5 moles of a thermally insulated (adiabatic) monatomic ideal gas is expanded from 0.10 m³ to 0.20 m³.  During the expansion, the pressure of the gas decreases from 3.039x10⁵ Pa to 0.957x10⁵ Pa

a. What is the initial temperature of the gas, before adiabatic expansion?

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b. What is the final temperature of the gas, after adiabatic expansion?

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c. What is the change in internal energy of the gas?

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d. How much heat is gained by the gas during this process?

Ans.  Q = 0 J (adiabatic process!)

e. How much work is performed by the gas during the heating process?

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6.  A sample of 5.0 moles of a thermally insulated (adiabatic) monatomic ideal gas is expanded from 0.10 m³ to 0.20 m³.  During the expansion, the temperature of the gas decreases from 800 K to 500 K.

a. What is the initial pressure of the gas, before adiabatic expansion?

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b. What is the final pressure of the gas, after adiabatic expansion?

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c. What is the change in internal energy of the gas?

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d. How much work is performed by the gas during the process?

Ans.