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 Multiple Choice QuestionsMultiple Choice Questions

1.

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume   and pressure. If the shell now undergoes an adiabatic expansion the relation between T and R is

  • T ∝ e-R

  • T ∝ e-3R

  • T ∝ (1/R)

  • T ∝(1/R3)

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2.

A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat.
(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies the same amount of heat. In both the cases body is brought from an initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is:

  • ln2,4ln2

  • ln2,ln2

  • ln2,2ln2

  • 2ln2,8ln2

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3.

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion the average time of collision between molecules increases as Vq , where V is the volume of the gas. The value of q is: open parentheses straight gamma space equals space straight C subscript straight p over straight C subscript straight v close parentheses

  • fraction numerator 3 straight gamma plus 5 over denominator 6 end fraction
  • fraction numerator 3 straight gamma minus 5 over denominator 6 end fraction
  • fraction numerator straight gamma plus 1 over denominator 2 end fraction
  • fraction numerator straight gamma plus 1 over denominator 2 end fraction
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4.

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in the figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

  • The change in internal energy in the process AB is -350 R.

  • The change in internal energy in the process BC is -500 R.

  • The change in internal energy in the whole cyclic process is 250 R.

  • The change in internal energy in the whole cyclic process is 250 R.

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5.

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

  • povo

  • open parentheses 13 over 2 close parentheses straight p subscript 0 straight v subscript 0
  • open parentheses 11 over 2 close parentheses straight p subscript straight o straight v subscript 0
  • open parentheses 11 over 2 close parentheses straight p subscript straight o straight v subscript 0
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6.

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

  • fraction numerator 1 over denominator 2 straight pi end fraction fraction numerator straight A subscript straight gamma straight p subscript 0 over denominator straight V subscript 0 straight M end fraction
  • fraction numerator 1 over denominator 2 straight pi end fraction fraction numerator straight V subscript 0 Mp subscript 0 over denominator straight A squared straight gamma end fraction
  • fraction numerator 1 over denominator 2 straight pi end fraction square root of fraction numerator straight A squared γp subscript 0 over denominator MV subscript 0 end fraction end root
  • fraction numerator 1 over denominator 2 straight pi end fraction square root of fraction numerator straight A squared γp subscript 0 over denominator MV subscript 0 end fraction end root
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7.

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

  • the efficiency of Carnot engine cannot be made larger than 50%

  • 1200 K

  • 750 K 

  • 750 K 

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8.

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in the figure. Efficiency of this cycle is nearly:(Assume the gas to be close to ideal gas)

  • 15.4%

  • 9.1%

  • 10.5%

  • 10.5%

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9.

Three perfect gases at absolute temperature T1, T2 and T3 are mixed. The masses of molecules are m1,m2 and m3 and the number of molecules is n1,n2 and n3 respectively.Assuming no loss of energy, the final temperature of the mixture is

  • fraction numerator straight n subscript 1 straight T subscript 1 plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 over denominator straight n subscript 1 plus space straight n subscript 2 plus space straight n subscript 3 end fraction
  • fraction numerator straight n subscript 1 straight T subscript 1 superscript 2 space plus straight n subscript 2 straight T subscript 2 superscript 2 space plus straight n subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction
  • fraction numerator straight n squared subscript 1 straight T subscript 1 superscript 2 space plus straight n squared subscript 2 straight T subscript 2 superscript 2 space plus straight n squared subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction
  • fraction numerator straight n squared subscript 1 straight T subscript 1 superscript 2 space plus straight n squared subscript 2 straight T subscript 2 superscript 2 space plus straight n squared subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction
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10.

A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then T1 and T2 are, respectively

  • 372 K and 330 K

  • 330 K and 268 K

  • 310 K and 248 K

  • 310 K and 248 K


D.

310 K and 248 K

The efficiency  is given by,

straight eta subscript 1 space equals space 1 space minus straight T subscript 2 over straight T subscript 1
rightwards double arrow space 1 over 6 space equals space 1 space minus space straight T subscript 2 over straight T subscript 1
rightwards double arrow space straight T subscript 2 over straight T subscript 1 space equals space 5 over 6
straight eta subscript 2 space equals space 1 minus fraction numerator straight T subscript 2 minus 62 over denominator straight T subscript 1 end fraction space space.... space left parenthesis straight i right parenthesis
1 third space equals space 1 minus fraction numerator straight T subscript 2 minus 62 over denominator straight T subscript 1 end fraction space... space left parenthesis ii right parenthesis
On space solving space Eqs space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
straight T subscript 1 space equals space 372 space straight K space and space straight T subscript 2 space equals space 310 space straight K

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