The volumetric properties of two
gases M and N are described by the generalized compressibility chart which
expresses the compressibility factor (Z) as a function of reduced pressure and
reduced temperature only. The operating pressure (P) and temperature (T) of two
gases M and N along with their critical properties (Pc and Tc)
are given in the table below.
ZM and ZN are
the compressibility factor of the gases M and N under the given operating
conditions, respectively.
The relation between ZM
and ZN is
(A)
ZM
= 8ZN
(B)
ZM
= 3ZN
(C)
ZM
= ZN
(D)
ZM
= 0.333ZN
GATE
2017
Answer: (C)
The pressure of a liquid is increased isothermally. The
molar volume of the liquid decreases from 50.45×10-6 m3/mol
to 48×10-6 m3/mol during this process. The isothermal
compressibility of the liquid is 109 Pa-1, which can be
assumed to be independent of pressure. The change in the molar Gibbs free
energy of the liquid, rounded to nearest integer, is _______ J/mol.
GATE
2017
Answer: 2450
The vapour pressure of a pure substance at a
temperature T is 30 bar. The actual and ideal gas values of g/RT for the
saturated vapour at this temperature T and 30 bar are 7.0 and 7.7 respectively.
Here, g is the molar Gibbs free energy and R is the universal gas constant. The
fugacity of the saturated liquid at these conditions, rounded to 1 decimal
place, is ____ bar.
GATE
2017
Answer: 14.89
Consider the
following properties:
(P) temperature (Q) specific
gravity
(R) chemical potential (S) volume
The
option which lists ALL the intensive properties is
(A) P (B) P and Q
(C) P, Q and R (D) P,
Q, R and s
GATE
2018
Answer: (C)
G
denotes the Gibbs free energy of a binary mixture, nT denotes the
total number of moles present in the system, μi is the chemical
potential of the ith component (μi ≠ 0 and μ1
>μ2) and xi is the mole fraction of the ith component.
The correct variation of G/nT (in J/mol) at constant temperature and
pressure is given by
GATE
2018
Answer: (C)
In a closed piston-cylinder system, methane was
observed to obey the following equation of state
P(V
- nb) = nRT
Where, b = 0.029 m3/mol. The temperature
and volume are 500°C and 5 m3 respectively for 100 moles of methane.
At this state of the system, the isobaric rate of change of temperature with
volume (in °C/m3) is __________ (rounded off to second decimal
place).
GATE
2018
Answer: 238.095
Consider a vessel containing steam
at 180 °C. The initial steam quality is 0.5 and the initial volume of the
vessel is 1 m3. The vessel loses heat at a constant rate q
under isobaric conditions so that the quality of steam reduces to 0.1 after 10
hours. The thermodynamic properties of water at 180 °C are (subscript g:
vapor phase; subscript f: liquid phase):
Specific
volume: vg = 0.19405 m3/kg,
vf = 0.001127 m3/kg
Specific
internal energy: ug = 2583.7 kJ/kg, uf = 762.08 kJ/kg
Specific
enthalpy: hg = 22778.2 kJ/kg, hf = 763.21 kJ/kg
The rate of heat loss q (in
kJ/hour) is___________(rounded off to the nearest integer).
GATE
2019
Answer: 825.92
Consider a
rigid, perfectly insulated, container partitioned into two unequal parts by a
thin membrane (see figure). One part contains one mole of an ideal gas at
pressure Pi and temperature Ti while the other part is
evacuated. The membrane ruptures, the gas fills the entire volume and the
equilibrium pressure is Pf = Pi/4. If Cp
(molar specific heat capacity at constant pressure), Cv (molar
specific heat capacity at constant volume) and r (universal gas constant) have
the same units as molar entropy, the change in molar entropy (Sf-Si)
is
(A)
Cp ln2 + R ln4
(B)
–Cv ln2 + R ln4
(C)
R ln4
(D)
Cp ln2
GATE
2019
Answer: (C)
For a binary
nonideal A-B mixture exhibiting a minimum boiling azeotrope, the activity
coefficient, γi (i = A, B), must satisfy
(A)
γA>1, γB>1
(B)
γA<1, γB>1
(C)
γA=1, γB=1
(D)
γA<1, γB<1
GATE
2019
Answer: (A)
A thermocouple senses temperature
based on the
(A) Nernst Effect
(B) Maxwell effect
(C) Seebeck effect
(D) Peltier effect
GATE
2019
Answer: (C)
Carbon monoxide (CO) reacts with
hydrogen sulphide (H2S) at a constant temperature of 800 K and a constant pressure
of 2 bar as:
The Gibbs free energy of the reaction Δgorxn = 22972.3
J/mol and universal gas constant R = 8.314 J/(mol K). Both the reactants and products
can be assumed to be ideal gases. If initially only 4 mol of H2S and
1 mol of CO are present, the extent of the reaction (in mol) at equilibrium
is_________ (rounded off to two decimal places).
GATE
2019
Answer: 0.29
For a single
component system, vapour (subscript g) and liquid (subscript f) coexist in
mechanical, thermal and phase equilibrium when
(A)
ug = uf (equality
of specific internal energy)
(B)
hg = hf (equality
of specific enthalpy)
(C)
sg = sf (equality
of specific entropy)
(D)
gg = gf (equality
of specific Gibbs free energy)
GATE
2019
Answer: (D)
Consider two
Carnot engines C1 and C2 as shown in the figure.
The
efficiency of the engines C1 and C2 are 0.40 and 0.35,
respectively. If the temperature of Reservoir R1 is 800 K, then the
temperature (in K) of Reservoir R3 is ______ (round of to nearest
integer).
GATE
2020
Answer: 312 K
Consider one
mole of an ideal gas in a closed system. It undergoes a change in state from L
to N through two different non-isothermal processes, as shown in the P-V
diagram (Where P is the pressure and V is the molar volume of the gas). Process
I is carried out in a single step, namely LN, whereas process II is carried out
in two steps, namely LM and MN. All the steps are reversible.
The
net heat flowing into the system for process I is QI and that for
process II is QII. The value of QI – QII (in
J) is
(A)
250
(B)
500
(C)
1000
(D)
1500
GATE
2020
Answer: (B)
A pure gas obeys
the equation of state given by
Where
P is the pressure, t is the absolute temperature, V is the molar volume of the
gas, R is the universal gas constant, and B is a parameter independent of T and
P. The residual molar Gibbs energy, GR, of the gas is given by the
relation
Where
Z is the compressibility factor and the integral is evaluated at constant T. If
the value of B is 1×10-4 m3 mol-1, the
residual molar enthalpy (in J mol-1) of the gas at 1000 kPa and 300
K is
(A)
100
(B)
300
(C)
2494
(D)
30000
GATE
2020
Answer: (A)
Mole fraction
and activity coefficient of component 1 in a binary liquid mixture are x1
and γ1, respectively. GE is excess molar Gibbs energy of the
mixture, R is universal gas constant and T is absolute temperature of the
mixture. Which one of the following is always true?
GATE
2020
Answer: (A)
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