GATE-CH-1991-7-i-td-2mark

For a gas obeying the van der Waals equation, at the critical temperature

• both $(\partial P/\partial V{)}_T$ and $({\partial }^{2}P/\partial V^2{)}_T$ are zero

• the first derivative is zero, while the second derivative is non-zero

• the second derivative is zero, while the first derivative is non-zero

• both the derivatives are non-zero

GATE-CH-1994-1-s-td-1mark

Ideal gas law is applicable at

• low $T$, low $P$

• high $T$, high $P$

• low $T$, high $P$

• high $T$, low $P$

GATE-CH-1995-1-l-td-1mark

A solid is transformed into vapor without going through the liquid phase at

• triple point

• boiling point

• below triple point

• always

GATE-CH-1999-1-7-td-1mark

Which of the following is true for virial equation of state?

• Virial coefficients are universal constants

• Virial coefficient $B$ represents three body interactions

• Virial coefficients are functions of temperature only

• For some gases, virial equations and ideal gas equations are the same

GATE-CH-2002-1-3-td-1mark

Which of the following conditions are satisfied at the critical point by the $PVT$ relation of a real fluid?

• ${\displaystyle {\left(\frac{{\partial }^{2}P}{\partial V^2}\right)}_T={\left(\frac{\partial P}{\partial V}\right)}_T=0}$

• ${\displaystyle {\left(\frac{{\partial }^{2}P}{\partial V^2}\right)}_T>0,{\left(\frac{\partial P}{\partial V}\right)}_T=0}$

• ${\displaystyle {\left(\frac{{\partial }^{2}P}{\partial V^2}\right)}_T<0,{\left(\frac{\partial P}{\partial V}\right)}_T=0}$

• ${\displaystyle {\left(\frac{{\partial }^{2}P}{\partial V^2}\right)}_T>0,{\left(\frac{\partial P}{\partial V}\right)}_T>0}$

GATE-CH-2006-35-td-2mark

The molar density of water vapor at the normal boiling point of water is 33 mol/m³. The compressibility factor under these conditions is close to which ONE of the following? $R=8.314$ J/(mol.K)

• 0.75

• 1

• 1.25

• 1.5

  Solution

GATE-CH-2007-8-td-1mark

Parameters '$a$' and '$b$’ in the van der Waals and other cubic equations of state represent

• $a$ - molecular weight;  $b$ - molecular polarity

• $a$ - molecular size;  $b$ - molecular attraction

• $a$ - molecular size;   $b$ - molecular speed

• $a$ - molecular attraction;  $b$ - molecular size

GATE-CH-2008-7-td-1mark

The work done by one mole of a van der Waals fluid undergoing reversible isothermal expansion from initial volume $V_i$ to final volume $V_f$ is

• ${\displaystyle RT\ln \left(\frac{V_f}{V_i}\right)}$

• ${\displaystyle RT\ln \left(\frac{V_f-b}{V_i-b}\right)}$

• ${\displaystyle RT\ln \left(\frac{V_f-b}{V_i-b}\right)-a(\frac{1}{V_f}-\frac{1}{V_i})}$

• ${\displaystyle RT\ln \left(\frac{V_f-b}{V_i-b}\right)+a(\frac{1}{V_f}-\frac{1}{V_i})}$

  Solution

GATE-CH-2013-8-td-1mark

The units of the isothermal compressibility are

• m^-3

• Pa^-1

• m³.Pa^-1

• m^-3.Pa^-1

GATE-CH-2017-6-td-1mark

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 ($P_c,T_c$) are given below.

Gas	$P$ (bar)	$T$ (K)	$P_c$ (bar)	$T_c$ (K)
M	25	300	75	150
N	75	1000	225	500

$Z_{\text{M}}$ and $Z_{\text{N}}$ are the compressibility factor of the gases M and N under given operating conditions, respectively.

The relation between $Z_{\text{M}}$ and $Z_{\text{N}}$ is

• $Z_{\text{M}}=8Z_{\text{N}}$

• $Z_{\text{M}}=3Z_{\text{N}}$

• $Z_{\text{M}}=Z_{\text{N}}$

• $Z_{\text{M}}=0.333Z_{\text{N}}$

  Solution

GATE-XE-2008-G-14-td-2mark

Steam of quality 0.98 is present in two separate containers $A$ and $B$ at 300 kPa and 200 kPa, respectively. Specific volumes of steam in containers $A$ and $B$ initially are $V_{A_1}$ and $V_{B_1}$, respectively. Steam condenses at a constant pressure in such a way that the final quality of steam in both the containers are 0.01 and specific volumes of steam in containers $A$ and $B$ are $V_{A_2}$ and $V_{B_2}$ respectively. Which one of the following statements is true?

• $V_{A_1}>V_{B_1}$ & $V_{A_2}>V_{B_2}$

• $V_{A_1}<V_{B_1}$ & $V_{A_2}<V_{B_2}$

• $V_{A_1}>V_{B_1}$ & $V_{A_2}<V_{B_2}$

• $V_{A_1}<V_{B_1}$ & $V_{A_2}>V_{B_2}$

  Solution

GATE-XE-2011-E-9-td-1mark

Consider three identical tanks A, B and C shown below. What is the pressure ($P$) in Tank C ?

• 1 bar

• 1.5 bar

• 2 bar

• 2.5 bar

  Solution

GATE-XE-2018-E-5-td-1mark

The value of the compressibility factor at the critical point evaluated using the van der Waals equation of state is

• $2/7$

• $5/8$

• $3/8$

• $1/7$

  Solution

GATE-CH-1993-6-6-td-1mark

A vessel of volume 1.0 m${}^3$ contains a mixture of liquid water and steam in equilibrium at 1.0 bar. Given that 90% of the volume is occupied by the steam, find the dryness fraction of the mixture.
Assume, at 1 bar, $V_L=0.001$ m${}^3$/kg and $V_V=1.7$ m${}^3$/kg.

• Answer
• Solution

GATE-CH-1993-6-8-td-2mark

In the vicinity of the triple point, the vapor pressures of liquid and solid ammonia are respectively given by $$\ln P=15.16-\frac{3063}{T}\text{ and }\ln P=18.70-\frac{3754}{T}$$ where $P$ is in atmospheres and $T$ is in Kelvin.
(i) What is the temperature (in K) at the triple point?
{#1}

(ii) What is the triple point pressure (in atm)?
{#2}

Solution

GATE-CH-2004-42-td-2mark

A vessel of volume 1000 m³ contains air which is saturated with water vapor. The total pressure and temperature are 100 kPa and 20^oC, respectively. Assuming that the vapor pressure of water at 20^oC is 2.34 kPa, the amount of water vapor (in kg) in the vessel is approximately

• 17

• 20

• 25

• 34

  Solution

0200-1-td-5mark

Calculate the molar volume of saturated liquid and saturated vapor of propane at 40${}^{\circ }$C and saturation pressure of 13.71 bar, using (i) ideal gas equation (ii) van der Waals equation (iii) Redlich-Kwong equation. $T_c=369.8$ K; $P_c=42.5$ bar. 

• Answer
• Solution