NEET UG - Equation of state of a perfect gas, work done on compressing a gas Online Test (MCQ Quiz)

1. What is the ideal gas law that relates pressure, volume, temperature, and the number of moles of a gas?

A) PV = nRT B) PV = mRT C) PV = nKT D) PV = mKT

2. In the ideal gas law PV = nRT, what does 'R' represent?

A) The ideal gas constant B) The universal gas constant C) The Boltzmann constant D) The specific gas constant

3. What is the value of the universal gas constant (R) in SI units (J/mol·K)?

A) 8.314 B) 1.987 C) 0.0821 D) 1.38 x 10^-23

4. Which of the following conditions must be met for a gas to be considered 'ideal'?

A) Intermolecular forces are negligible and molecular volume is negligible compared to the volume of the container. B) Intermolecular forces are strong and molecular volume is significant. C) The gas must be monatomic and at high pressure. D) The gas must be diatomic and at low temperature.

5. The equation of state for a perfect gas is derived from which two gas laws?

A) Boyle's Law and Charles's Law B) Gay-Lussac's Law and Avogadro's Law C) Charles's Law and Avogadro's Law D) Boyle's Law and Gay-Lussac's Law

6. Boyle's Law states that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. Mathematically, this is expressed as:

A) P ∝ 1/V B) V ∝ 1/P C) P ∝ V D) V ∝ P

7. Charles's Law states that for a fixed mass of gas at constant pressure, volume is directly proportional to its absolute temperature. Mathematically, this is expressed as:

A) V ∝ T B) T ∝ V C) V ∝ 1/T D) T ∝ 1/V

8. Avogadro's Law states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules. This implies:

A) V ∝ n (at constant P and T) B) n ∝ V (at constant P and T) C) V ∝ 1/n (at constant P and T) D) n ∝ 1/V (at constant P and T)

9. If the temperature of an ideal gas is kept constant, and its volume is halved, what happens to its pressure?

A) It doubles B) It halves C) It remains the same D) It quadruples

10. If the pressure of an ideal gas is kept constant, and its absolute temperature is doubled, what happens to its volume?

A) It doubles B) It halves C) It remains the same D) It quadruples

11. What is the work done when a gas is compressed isothermally from an initial volume V1 to a final volume V2?

A) W = nRT ln(V2/V1) B) W = nRT ln(V1/V2) C) W = P(V2 - V1) D) W = nCv(T2 - T1)

12. In the formula for isothermal work done, W = nRT ln(V1/V2), what does V1 represent?

A) Initial volume B) Final volume C) Change in volume D) Average volume

13. For work done *on* a gas during compression, the work done is typically considered:

A) Positive B) Negative C) Zero D) Dependent on temperature

14. When a gas is compressed adiabatically, what happens to its temperature?

A) It increases B) It decreases C) It remains constant D) It depends on the pressure

15. What is the work done when a gas is compressed isobarically (at constant pressure) from volume V1 to V2?

A) P(V2 - V1) B) P(V1 - V2) C) nRT ln(V2/V1) D) nCv(T2 - T1)

16. If a gas is compressed at constant volume (isochoric process), what is the work done on the gas?

A) Zero B) Positive C) Negative D) Depends on temperature

17. The work done on compressing a gas is given by the integral ∫ P dV. During compression, dV is:

A) Negative B) Positive C) Zero D) Constant

18. Consider a gas compressed from V1 to V2 (V2 < V1) at constant temperature. The work done *by* the gas is:

A) Negative B) Positive C) Zero D) Infinite

19. If a gas is compressed from 5 L to 2 L at a constant pressure of 2 atm, what is the work done on the gas in L·atm?

A) 6 L·atm B) -6 L·atm C) 3 L·atm D) -3 L·atm

20. What is the relationship between pressure (P), volume (V), and absolute temperature (T) for a fixed amount of an ideal gas?

A) PV/T = constant B) PT/V = constant C) VT/P = constant D) P/VT = constant

21. What is the work done in compressing a gas from volume V1 to V2 (V2 < V1) isothermally?

A) nRT ln(V1/V2) B) nRT ln(V2/V1) C) P(V1 - V2) D) Zero

22. In the equation PV = nRT, if n and T are constant, then PV = constant. This is a statement of:

A) Boyle's Law B) Charles's Law C) Gay-Lussac's Law D) Avogadro's Law

23. What is the work done on a gas during an isochoric process where the volume is constant?

A) 0 B) Positive C) Negative D) Depends on pressure change

24. If a gas is compressed such that its volume decreases, the work done *on* the gas is generally:

A) Positive B) Negative C) Zero D) Uncertain without temperature

25. The equation of state for a perfect gas can also be written as PV = NkBT, where kB is:

A) Boltzmann constant B) Universal gas constant C) Specific gas constant D) Planck's constant

26. What is the work done on a gas when it is compressed from 10 L to 5 L at a constant pressure of 1 atm?

A) 5 L·atm B) -5 L·atm C) 10 L·atm D) -10 L·atm

27. For a fixed amount of gas, which of the following is constant?

A) PV/T B) PT/V C) VT/P D) P/VT

28. During an isothermal compression of an ideal gas, heat is:

A) Removed from the gas B) Added to the gas C) Not involved D) Generated internally

29. If the volume of a gas is reduced by half at constant temperature, the new pressure will be:

A) Twice the original pressure B) Half the original pressure C) The same as the original pressure D) Four times the original pressure

30. Work done on a gas during adiabatic compression is always accompanied by:

A) An increase in internal energy B) A decrease in internal energy C) No change in internal energy D) A decrease in temperature

31. What is the unit of work done in the context of gas compression in SI units?

A) Joule (J) B) Pascal (Pa) C) Newton (N) D) Watt (W)

32. Which process involves no heat exchange with the surroundings?

A) Adiabatic B) Isothermal C) Isobaric D) Isochoric

33. The work done by a gas during expansion is positive. Therefore, the work done *on* the gas during compression is:

A) Negative B) Positive C) Zero D) Equal in magnitude

34. The equation of state PV = nRT is valid for:

A) Ideal gases only B) Real gases at high pressure C) Real gases at low temperature D) All gases under all conditions

35. If a gas expands from V1 to V2 (V2 > V1) at constant pressure P, the work done *by* the gas is:

A) P(V2 - V1) B) P(V1 - V2) C) nRT ln(V2/V1) D) Zero

36. What is the work done on a gas compressed from 4 L to 1 L at a constant pressure of 3 atm?

A) 9 L·atm B) -9 L·atm C) 3 L·atm D) -3 L·atm

37. In the isothermal compression formula W = nRT ln(V1/V2), if V1 > V2, the term ln(V1/V2) is:

A) Positive B) Negative C) Zero D) Undefined

38. What does the area under the P-V curve represent?

A) Work done B) Heat transfer C) Change in internal energy D) Change in temperature

39. For a given change in volume, which process requires the most work done *on* the gas for compression?

A) Adiabatic B) Isothermal C) Isobaric D) Isochoric

40. The work done in compressing a gas isothermally is W = nRT ln(V1/V2). If the number of moles (n) increases, what happens to the work done for the same compression ratio?

A) Increases B) Decreases C) Remains the same D) Becomes zero

41. If a gas is compressed from 10 m³ to 5 m³ at a constant pressure of 100 kPa, what is the work done on the gas in Joules?

A) 500,000 J B) -500,000 J C) 1,000,000 J D) -1,000,000 J

42. Which of the following is NOT a fundamental assumption of the kinetic theory of gases that leads to the ideal gas law?

A) Gas molecules are in constant, random motion. B) The volume occupied by the gas molecules themselves is negligible compared to the total volume of the container. C) Intermolecular forces are attractive and significant. D) Collisions between molecules and with the walls are perfectly elastic.

43. If a gas is compressed isothermally, its internal energy:

A) Remains constant B) Increases C) Decreases D) Depends on the gas type

44. What is the relationship between the universal gas constant (R) and the Boltzmann constant (kB)?

A) R = NA * kB, where NA is Avogadro's number B) kB = NA * R C) R = NA / kB D) kB = R / NA

45. A gas is compressed from 10 L to 5 L. If this process is done rapidly, it is likely to be closer to which type of process?

A) Adiabatic B) Isothermal C) Isobaric D) Isochoric

46. The work done on a gas during compression is given by -∫ P dV. If the pressure is constant, P, and the volume changes from V1 to V2, the work done on the gas is:

A) -P(V2 - V1) B) P(V2 - V1) C) -P(V1 - V2) D) P(V1 - V2)

47. What is the work done on a gas when it is compressed from 8 L to 2 L at a constant pressure of 5 atm?

A) 30 L·atm B) -30 L·atm C) 6 L·atm D) -6 L·atm

48. For an ideal gas, the internal energy depends only on:

A) Temperature B) Pressure C) Volume D) Number of moles

49. Which gas law directly relates the number of moles of a gas to its volume at constant temperature and pressure?

A) Avogadro's Law B) Boyle's Law C) Charles's Law D) Gay-Lussac's Law

50. The work done on a gas during an isothermal process is given by W = nRT ln(V1/V2). If the temperature (T) is increased, for the same initial and final volumes, the work done on the gas will:

A) Increase B) Decrease C) Remain the same D) Become zero

Equation of state of a perfect gas, work done on compressing a gas - Online Test

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