For the given $P-V$ diagram of a thermodynamic system,match the curves with their respective thermodynamic processes. ($P$ = Pressure and $V$ = Volume)
CurveProcess
$I$$a)$ Adiabatic
$II$$b)$ Isobaric
$III$$c)$ Isochoric
$IV$$d)$ Isothermal

  • A
    $I-c, II-a, III-d, IV-b$
  • B
    $I-c, II-d, III-b, IV-a$
  • C
    $I-d, II-b, III-a, IV-c$
  • D
    $I-a, II-c, III-d, IV-b$

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Consider the following volume-temperature $(V-T)$ diagram for the expansion of $5$ moles of an ideal monoatomic gas. Considering only $P-V$ work is involved,the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$ [Use the given data: Molar heat capacity of the gas for the given temperature range,$C_{v,m} = 12 \ J \ K^{-1} \ mol^{-1}$ and gas constant,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]

$A$ cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in the figure.
$A$ to $B$: volume constant
$B$ to $C$: adiabatic
$C$ to $D$: volume constant
$D$ to $A$: adiabatic
$V_C = V_D = 2V_A = 2V_B$
$(a)$ In which part of the cycle is heat supplied to the engine from outside?
$(b)$ In which part of the cycle is heat given to the surrounding by the engine?
$(c)$ What is the work done by the engine in one cycle? Write your answer in terms of $P_A, P_B, V_A$.
$(d)$ What is the efficiency of the engine?
$(\gamma = 5/3, C_v = 3/2 R$ for one mole of the gas$)$

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Match List-$I$ with List-$II$.
List-$I$List-$II$
$(A)$ Isothermal$(I)$ $\Delta W = 0$
$(B)$ Adiabatic$(II)$ $\Delta Q = 0$
$(C)$ Isobaric$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric$(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

Match the following $:-$
Column-$I$ Column-$II$
$(i)$ Adiabatic process $(a)$ Constant temperature
$(ii)$ Isolated system $(b)$ No exchange of energy and matter
$(iii)$ Isothermal change $(c)$ First law of thermodynamics
$(iv)$ Law of conservation of energy $(d)$ No transfer of heat only

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