Practice MCQ on Gas Laws and Laws of Thermodynamics with Answers

**MCQ on Gas Laws and Laws of Thermodynamics with Answers**

**Q1. An ideal gas expands in a process in which its pressure depends on the volume as p = p _{o}e^{-αv} , where p_{o} and α are two positive constants. If n is the number of moles in the gas, the maximum temperature that it will attain in this process is (R is the universal gas constant)**

(a) p_{o}/eαnR

(b) p_{o}/αn^{3}R

(c) ep_{o}/αnR

(d) (p_{o})^{2}/αnR

**Q2. Two identical containers A and B are connected by a small tube with a value that allows gas flow when the pressure difference across it is greater than 0.6 atm. Initially, A contains an ideal gas at pressure 0.5 atm and B a vacuum with the entire system at 27 ^{o}C. The System is now heated to a temperature of 207^{o}C. What is the final Pressure in B?**

(a) 1 atm

(b) 0.7 atm

(c) 0.4 atm

(d) 0.1 atm

**Q3. One mole of a gas is contained in a closed vessel of volume 0.25 L. It is assumed to obey van der** Waal’s equation of 90 atm. As the pressure is increased to 100 atm at 300K, its temperature rises to 325 K . Calculate the value of van der** Waal’s constants a and b.**

(a) 1.6 Å

(b) 3.2 Å

(c) 16 Å

(d) 32 Å

**Q4. The critical temperature of a van der Waal’s gas is**

(a) 3b

(b) ^{8a}/_{27Rb}

(c) ^{8a}/_{27b}

(d) ^{a}/_{27b2}

**Q5. If the equilibrium state of the vapour near and above the critical point is described by the Van der Waal equation of state (p+ ^{a}/_{ν2} )(ν-b) = RT, where ν = ^{V}/_{n} is the molar volume, which of the following statements about the critical values of (molar) volume, pressure and temperature at the critical points are true? **

(a) ∂p/_{∂ν} |_{T=Tc} = 0

(b) ∂p/_{∂ν} |_{T=Tc} = 0 ; ∂^{2}p/_{∂ν2} |_{T=Tc} > 0

(c) ∂p/_{∂ν} |_{T=Tc} = 0 ; ∂^{2}p/_{∂ν2} |_{T=Tc} < 0

(d) ∂p/_{∂ν} |_{T=Tc} = 0 ; ∂^{2}p/_{∂ν2} |_{T=Tc} = 0

**Q6. Calculate Van der** **Waal’s constants a and b, if T _{c} = 5.3 K and P_{c} = 2.25 K atm**

(a) 3.59 × 10^{-3} Nm^{4}mol^{-2} and 2.42 × 10^{-5} m^{3}mol^{-1}

(b) 3.59 × 10^{-2} Nm^{4}mol^{-2} and 2.42 × 10^{-3} m^{3}mol^{-1}

(c) 3.59 × 10^{-5} Nm^{4}mol^{-2} and 2.42 × 10^{-5} m^{3}mol^{-1}

(d) 3.59 × 10^{-3} Nm^{4}mol^{-5} and 2.42 × 10^{-3} m^{3}mol^{-1}

**Q7. Scientists make an insulated container to hold 4.0 moles of nitrogen at a pressure of 10 ^{5} Pa and a temperature of 200 K. What is the approximate size of the container? (1atm = 101 kP_{a}) **

(a) 4 litres

(b) 8 litres

(c) 17 litres

(d) 67 litres

**Q8. If the volume of a closed system containing an ideal gas is held constant and its temperature is increased, the pressure inside the system **

(a) increases

(b) remains constant

(c) decreases

(d) will change based on the chemical nature of the substance inside

**Q9. Two vessels separately contain two ideal gas A and B at the same temperature, the pressure of A being twice that of B. Under these conditions, the density of A is found to be one and half times the density of B. The ratio of molecular weights of A and B is **

(a) ^{1}/_{2}

(b) ^{2}/_{3}

(c) ^{3}/_{4}

(d) 2

**Q10. An ideal gas undergoes a process during which P√V is constant, where P is the pressure and V is the volume of the gas. If volume of the gas decrease to ^{1}/_{4} th of its initial value, then the temperature of the gas will become**

(a) decrease of half of it initial value

(b) increase to double of its initial value

(c) remains constant

(d) increase by four times

**Q11. The relation between pressure and volume of an ideal gas in a reversible process is given by P = aV+b , where a = – ^{31}/_{56} Pascal/meter^{3} , b = ^{255}/_{7} Pascals. The volume at which the temperature attains maximum value is**

(a) 32.9 m^{3}

(b) 329.7 m^{3}

(c) 0.329 m^{3}

(d) 20.7 m^{3}

**Q12. A monoatomic gas is described by the equation of state p(V-bn) = nRT , where b and R are constants and other quantities have their usual meanings. The maximum density (in moles per unit volume) to which this gas can be compressed is **

(a) ^{1}/_{bn}

(b) b

(c) ^{1}/_{b}

(d) infinity

**Q13. Let ΔW be the work done in an infinitesimal reversible process. Which of the following statement is correct? **

(a) ΔW is a perfect differential only in an adiabatic process

(b) ΔW is not a perfect differential for all process

(c) ΔW is a perfect differential for all process

(d) ΔW is a perfect differential only for an isothermal process

**Q14. Let ΔW denote the work done in an infinitesimal quasi-static reversible thermodynamics process ΔW**

**is**

(a) not a perfect differential for any process

(b) a perfect differential only for an adiabatic process

(c) a perfect differential for all process

(d) a perfect differential for an isothermal process

**Q15. There are two systems A and B at temperatures** T_{1} and T_{2} (T_{2} > T_{1}) respectively. They are kept in thermal Equilibrium and their final temperature becomes T_{f} . Which of the following option is correct**?**

(a) T_{1} < T_{f} < T_{2}

(b) T_{1} > T_{f} < T_{2}

(c) T_{f} = (T_{1}+T_{2} )/_{2}

(d) None

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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (a) | 06. | (a) | 11. | (a) |

02. | (d) | 07. | (d) | 12. | (c) |

03. | (b) | 08. | (a) | 13. | (a) |

04. | (b) | 09. | (c) | 14. | (a) |

05. | (d) | 10. | (a) | 15. | (b) |