Kinetic Theory of Gases Mock Test

Kinetic Theory of Gases Mock Test

Complete Practice Test with Detailed Explanations

Test Instructions

1. This test contains 10 Multiple Choice Questions, 10 Numerical Problems, and 5 Short Answer Questions.

2. For MCQs, select the correct option. Each MCQ carries 1 mark.

3. For numerical problems, solve and find the answer. Each numerical problem carries 2 marks.

4. For short answer questions, write concise answers. Each short answer question carries 2 marks.

5. Total marks: 10 (MCQs) + 20 (Numericals) + 10 (Short Answers) = 40 marks.

6. After completing the test, check the detailed explanations provided at the end.

Section A: Multiple Choice Questions (10 × 1 = 10 Marks)

1. The kinetic theory of gases assumes that:
A. Gas molecules are in random motion
B. Gas molecules exert forces on each other only during collisions
C. The volume of gas molecules is negligible compared to the container volume
D. All of the above
2. The average kinetic energy of gas molecules is directly proportional to:
A. Pressure of the gas
B. Volume of the gas
C. Absolute temperature of the gas
D. Density of the gas
3. According to kinetic theory, pressure exerted by an ideal gas is due to:
A. Attractive forces between molecules
B. Collisions of molecules with the walls of container
C. Repulsive forces between molecules
D. Gravitational pull
4. Root mean square speed of gas molecules depends on:
A. Pressure only
B. Temperature only
C. Both pressure and temperature
D. Volume only
5. At constant temperature, if pressure of a gas is doubled, its density:
A. Becomes half
B. Becomes double
C. Remains same
D. Becomes four times
6. The mean free path of gas molecules increases when:
A. Density increases
B. Temperature decreases
C. Pressure increases
D. Pressure decreases
7. The ratio of specific heats (Cp/Cv) for monatomic gases is:
A. 1.33
B. 1.40
C. 1.67
D. 1.50
8. Real gases behave like ideal gases at:
A. High pressure and low temperature
B. High pressure and high temperature
C. Low pressure and high temperature
D. Low pressure and low temperature
9. The average kinetic energy of oxygen molecules at 27°C is:
A. 6.21 × 10⁻²¹ J
B. 4.14 × 10⁻²¹ J
C. 5.65 × 10⁻²¹ J
D. 3.11 × 10⁻²¹ J
10. The speed of sound in a gas is related to:
A. Most probable speed
B. Average speed
C. Root mean square speed
D. All of the above

Section B: Numerical Problems (10 × 2 = 20 Marks)

1. Calculate the root mean square speed of oxygen molecules at 27°C. (Molecular weight of O₂ = 32 g/mol, R = 8.31 J/mol·K)
2. A gas at 2 atm pressure occupies 5 liters at 300 K. How many moles of gas are present? (R = 0.0821 L·atm/mol·K)
3. Calculate the average kinetic energy of helium molecules at 127°C. (k = 1.38 × 10⁻²³ J/K)
4. The density of a gas is 1.78 g/L at STP. Calculate its molar mass.
5. If the rms speed of hydrogen molecules at a certain temperature is 1800 m/s, find the temperature. (Molecular weight of H₂ = 2 g/mol, R = 8.31 J/mol·K)
6. Calculate the pressure exerted by 10²³ molecules of oxygen each of mass 5.3 × 10⁻²⁶ kg in a 2 liter container with rms speed 400 m/s.
7. A mixture of 2 moles of hydrogen and 3 moles of helium is at 300 K. Find the average kinetic energy per molecule of the mixture.
8. At what temperature will the rms speed of oxygen molecules be twice that at 27°C?
9. Calculate the ratio of most probable speed to average speed for a gas at a given temperature.
10. The mean free path of nitrogen molecules at STP is 6.0 × 10⁻⁸ m. If the radius of nitrogen molecule is 1.0 × 10⁻¹⁰ m, calculate the number of molecules per unit volume.

Section C: Short Answer Questions (5 × 2 = 10 Marks)

1. State the basic postulates of kinetic theory of gases.
2. Derive the expression for pressure exerted by an ideal gas.
3. Explain why the specific heat at constant pressure (Cp) is greater than specific heat at constant volume (Cv) for gases.
4. What is meant by mean free path of gas molecules? On what factors does it depend?
5. Distinguish between real gases and ideal gases. Give two examples of each.

परीक्षा निर्देश

1. इस परीक्षा में 10 बहुविकल्पीय प्रश्न, 10 संख्यात्मक समस्याएं और 5 लघु उत्तरीय प्रश्न हैं।

2. बहुविकल्पीय प्रश्नों के लिए, सही विकल्प चुनें। प्रत्येक बहुविकल्पीय प्रश्न 1 अंक का है।

3. संख्यात्मक समस्याओं के लिए, हल करें और उत्तर ज्ञात करें। प्रत्येक संख्यात्मक समस्या 2 अंक की है।

4. लघु उत्तरीय प्रश्नों के लिए, संक्षिप्त उत्तर लिखें। प्रत्येक लघु उत्तरीय प्रश्न 2 अंक का है।

5. कुल अंक: 10 (बहुविकल्पीय) + 20 (संख्यात्मक) + 10 (लघु उत्तरीय) = 40 अंक।

6. परीक्षा पूरी करने के बाद, अंत में दिए गए विस्तृत स्पष्टीकरण की जाँच करें।

खण्ड क: बहुविकल्पीय प्रश्न (10 × 1 = 10 अंक)

1. गैसों के गतिज सिद्धांत के अनुसार माना जाता है कि:
क. गैस के अणु यादृच्छिक गति करते हैं
ख. गैस के अणु केवल टक्करों के दौरान एक दूसरे पर बल डालते हैं
ग. गैस के अणुओं का आयतन पात्र के आयतन की तुलना में नगण्य होता है
घ. उपरोक्त सभी
2. गैस के अणुओं की औसत गतिज ऊर्जा सीधे आनुपातिक होती है:
क. गैस के दाब के
ख. गैस के आयतन के
ग. गैस के परम ताप के
घ. गैस के घनत्व के
3. गतिज सिद्धांत के अनुसार, आदर्श गैस द्वारा डाला गया दाब किसके कारण होता है?
क. अणुओं के बीच आकर्षक बल
ख. अणुओं का पात्र की दीवारों से टकराव
ग. अणुओं के बीच प्रतिकर्षी बल
घ. गुरुत्वाकर्षण खिंचाव
4. गैस के अणुओं का वर्ग माध्य मूल चाल निर्भर करता है:

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