Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Heat and Thermodynamics question

2017 · Shift 1 · Q52
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Advanced
  3. /Physics
  4. /Heat and Thermodynamics
  5. /2017 · Shift 1 · Q52

Heat and Thermodynamics question

2017 · Shift 1 · Q52

JEE AdvancedPhysicsHeat and ThermodynamicsMCQ+3 / −0.75
An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P−VP-VP−V diagram in column 3 of the table. Consider only the path from state 111 to state 2.W2.W2.W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here YYY is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.n.n.JEE Advanced 2017 Paper 1 Offline Physics - Heat and Thermodynamics Question 54 English Comprehension 1 JEE Advanced 2017 Paper 1 Offline Physics - Heat and Thermodynamics Question 54 English Comprehension 2Which of the following options is the only correct representation of a process in which ΔU=ΔQ−PΔV\Delta U = \Delta Q - P\Delta VΔU=ΔQ−PΔV?
  1. A
    (II)(iv)(R)\left( {{\rm I}{\rm I}} \right)\left( {iv} \right)\left( R \right)(II)(iv)(R)
  2. B
    (III)(iii)(P)\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)(III)(iii)(P)
  3. C
    (II)(iii)(S)\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( S \right)(II)(iii)(S)
  4. D
    (II)(iii)(P)\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)(II)(iii)(P)
View written solutionFree

Correct answer: D

  1. Interpret the condition

    We are asked to identify the process for which ΔU=ΔQ−PΔV.\Delta U = \Delta Q - P\Delta V.ΔU=ΔQ−PΔV.

    From the first law of thermodynamics, in differential form, δQ=dU+δW.\delta Q = dU + \delta W.δQ=dU+δW.

    If the work term is written as δW=P dV,\delta W = P\,dV,δW=PdV, then for a finite change along a path, ΔU=ΔQ−∫P dV.\Delta U = \Delta Q - \int P\,dV.ΔU=ΔQ−∫PdV.

    The given relation ΔU=ΔQ−PΔV\Delta U = \Delta Q - P\Delta VΔU=ΔQ−PΔV will be valid when PPP remains constant during the process from state 111 to state 222, so that ∫P dV=P∫dV=PΔV.\int P\,dV = P\int dV = P\Delta V.∫PdV=P∫dV=PΔV.

    Therefore, the required process must be an isobaric process.

  2. Find the correct equation set

    For an ideal gas in an isobaric process:

    • P=constantP = \text{constant}P=constant
    • From PV=nRTPV=nRTPV=nRT, V∝TV \propto TV∝T
    • Work done by gas: Wby=P(V2−V1)=PΔVW_{\text{by}} = P(V_2-V_1)=P\Delta VWby​=P(V2​−V1​)=PΔV
    • Heat supplied: Q=nCPΔTQ = nC_P\Delta TQ=nCP​ΔT
    • Change in internal energy: ΔU=nCVΔT\Delta U = nC_V\Delta TΔU=nCV​ΔT

    So among the equation labels, we must choose the one corresponding to constant pressure. In the table, that is represented by (II).

  3. Find the correct PPP-VVV plot

    An isobaric process on a PPP-VVV diagram is a horizontal line because pressure is constant while volume changes.

    Among the given graph labels, the horizontal line corresponds to (iii).

  4. Find the correct work expression

    Since the question says WWW denotes the work done on the system, for expansion, Won=−PΔV.W_{\text{on}} = -P\Delta V.Won​=−PΔV.

    The table’s corresponding work-expression label for isobaric process is (P).

  5. Match the triplet

    Hence the correct representation is (II)(iii)(P)\boxed{(II)(iii)(P)}(II)(iii)(P)​

  6. Check options

    • A: (II)(iv)(R)(II)(iv)(R)(II)(iv)(R) — incorrect graph/work
    • B: (III)(iii)(P)(III)(iii)(P)(III)(iii)(P) — incorrect process equation label
    • C: (II)(iii)(S)(II)(iii)(S)(II)(iii)(S) — incorrect work label
    • D: (II)(iii)(P)(II)(iii)(P)(II)(iii)(P) — correct

Therefore, the only correct option is D.

PreviousNext

More from Heat and Thermodynamics

  • An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P−V diagram in column 3 of the table. Consider only the path from state 1 to state 2.W denotes the corresponding work done on… Includes diagram2017 · MCQ
  • A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log2​(P0​P​), where P0 is a constant. When…2016 · Numerical
  • A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates… Includes diagram2016 · MCQ
  • A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi = 105 Pa and volume Vi = 10-3 m3 changes to a final state at Pf = (321​)×105Pa and…2016 · MCQ
  • The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10oC. Now the end P is maintained at 10oC, while the end S is heated and maintained at 400oC. The system is…2016 · MCQ
  • Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 104 times the power emitted from B. The ratio (λB​λA​​) of their wavelengths λA​…2015 · Numerical
  • A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are)2015 · Multiple correct
  • An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then… Includes diagram2015 · Multiple correct