[Free] IIT JAM Physics Test Series 2023 : Kinetic Theory and Thermodynamics – The Gas Laws and Laws of Thermodynamics

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[Free] IIT JAM Physics Test Series 2023 : Kinetic Theory and Thermodynamics- (The Gas Laws and Laws of Thermodynamics

Q1. An ideal gas expands in a process in which its pressure depends on the volume as p = poe-αv , where po 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) po/eαnR
(b) po/αn3R
(c) epo/αnR
(d) (po)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 27oC. The System is now heated to a temperature of 207oC. 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 vander 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 vander 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 vander 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 is true ?

(a) ∂p/∂ν |T=Tc = 0
(b) ∂p/∂ν |T=Tc = 0 ; ∂2p/∂ν2 |T=Tc > 0
(c) ∂p/∂ν |T=Tc = 0 ; ∂2p/∂ν2 |T=Tc < 0
(d) ∂p/∂ν |T=Tc = 0 ; ∂2p/∂ν2 |T=Tc = 0

Q6. Calculate vander waal’s constants a and b, if Tc = 5.3 K and Pc = 2.25 K atm

(a) 3.59 × 10-3 Nm4mol-2 and 2.42 × 10-5 m3mol-1
(b) 3.59 × 10-2 Nm4mol-2 and 2.42 × 10-3 m3mol-1
(c) 3.59 × 10-5 Nm4mol-2 and 2.42 × 10-5 m3mol-1
(d) 3.59 × 10-3 Nm4mol-5 and 2.42 × 10-3 m3mol-1

Q7. Scientists make an insulated container to hold 4.0 moles of nitrogen at a pressure of 105 Pa and a temperature of 200 K. What is the approximate size of the container ? (1atm = 101 kPa)

(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/meter3 , b = 255/7 Pascals. The volume at which the temperature attains maximum value is

(a) 32.9 m3
(b) 329.7 m3
(c) 0.329 m3
(d) 20.7 m3

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 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 temperature T1 and T2 (T2 > T1) respectively. They are kept in thermal Equilibrium and their final temperature becomes Tf . Which of the following option is correct ?

(a) T1 < Tf < T2
(b) T1 > Tf < T2
(c) Tf = (T1+T2 )/2
(d) None

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