GATE Overflow for GATE XE - Recent activity in Thermodynamics, Kinetics and Phase Transformations

Edited: GATE XE 2026 | Question: 180

Thu, 02 Apr 2026 11:16:20 +0000

A fuel with composition by mass is given as $78 \%$ carbon $(\mathrm{C}), 16 \%$ hydrogen $\left(\mathrm{H}_{2}\right)$, $3.2 \%$ sulphur $(\mathrm{S}), 1.6 \%$ oxygen $\left(\mathrm{O}_{2}\right)$, and ash. The fuel is fired in a boiler with excess air for the complete combustion and no carbon monoxide $\text{(CO)}$ is detected in the flue gases. The dry flue gas contains $0.2 \%$ sulphur dioxide $\left(\mathrm{SO}_{2}\right)$ by volume. Which one of the following options is closest to the amount of excess air provided (in $\%$ by mass)?

Assume molar masses $\left(\mathrm{g} \mathrm{~mol}^{-1}\right)$ of $\mathrm{C}, \mathrm{H}_{2}, \mathrm{~S}$, and $\mathrm{O}_{2}$ are $12,2,32$, and 32 , respectively, and the volumetric ratio of nitrogen $\left(\mathrm{N}_{2}\right)$ and oxygen $\left(\mathrm{O}_{2}\right)$ in the air as $3.76:1$.

$14.8$
$7.4$
$22.2$
$3.1$

Edited: GATE XE 2026 | Question: 96

Thu, 02 Apr 2026 06:18:17 +0000

A rigid spherical solid ball at $1000^{\circ} \mathrm{C}$ is cooled slowly to $200^{\circ} \mathrm{C}$ in a surrounding air at $25^{\circ} \mathrm{C}$. The density, specific heat capacity, and diameter of the ball are $8000 \mathrm{~kg} / \mathrm{m}^{3}, 500 \mathrm{~J} / \mathrm{kg}-\mathrm{K}$, and $10$ $\mathrm{mm}$; respectively. Assuming that the cooling process is quasi-equilibrium, the entropy generated (in $\mathrm{J/K}$) in the process is $\_\_\_\_$ (rounded off to two decimal places).

Edited: GATE XE 2026 | Question: 93

Wed, 01 Apr 2026 09:02:38 +0000

Consider a single component fluid at saturation conditions having the following properties.

Latent heat of vaporization, $h_{f g}=39.6 \times 10^{3} \mathrm{~kJ} / \mathrm{kmol}$

Compressibility factor for the vapor phase, $z_{g}=\dfrac{v_{g}}{v_{\text{ideal}}}=\dfrac{P_{\text {sat }} v_{g}}{R_{u} T}=0.95$

$P_{\text {sat }}$ is the saturation pressure

$T$ is the temperature

$v_{g}$ is the molar specific volume of the vapor phase

Assume that $v_{f g}=v_{g}$, where $v_{f g}$ is the difference in the molar specific volume of the vapor and the liquid phases

Universal gas constant, $R_{u}=8.314 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}$

Using the Clapeyron equation, the quantity $-\left.\dfrac{d \ln P}{d(1 / T)}\right|_{\text {saturation }}$ (in $\mathrm{K}$) is $\_\_\_\_$ (rounded off to two decimal places).

Edited: GATE XE 2026 | Question: 83

Wed, 01 Apr 2026 08:39:11 +0000

A stream of moist air at $101$ $\mathrm{kPa}$ and $25^{\circ} \mathrm{C}$ undergoes a constant pressure process such that its dry bulb temperature increases and specific humidity decreases. For this process, which of the following statements is/are always CORRECT?

Wet bulb temperature increases.
Dew point temperature decreases.
Relative humidity decreases.
Adiabatic saturation temperature increases.

Edited: GATE XE 2026 | Question: 43

Tue, 31 Mar 2026 09:42:41 +0000

Three phases, $\alpha, \beta$ and $\mathrm{L}$ are shown in the binary phase diagram below. Identify the correct $\mathrm{G-X}$ (Gibbs free energy vs Composition) plot corresponding to temperature $\mathrm{T}_{0}$.

Edited: GATE XE 2026 | Question: 40

Tue, 31 Mar 2026 08:33:32 +0000

The degrees of freedom of a system with $2$ components and $2$ phases in equilibrium is $\_\_\_\_$ (answer in integer).

Edited: GATE XE 2025 | Question: 102

Mon, 30 Jun 2025 08:18:24 +0000

Air at $101 \: \mathrm{kPa}$, $15^{\circ} \mathrm{C}$ and $50 \%$ relative humidity is first heated to $20^{\circ} \mathrm{C}$ in a heating coil, and then humidified by spraying water on it. In the final state, the air has temperature of $25^{\circ} \mathrm{C}$ and relative humidity of $85 \%$. The amount of water sprayed (in $\mathrm{gm}$ per $\mathrm{kg}$ of dry air) is $\_\_\_\_\_\_$ (rounded off to two decimal places).

Use the following data: The saturation pressure of water at $15^{\circ} \mathrm{C}=1.7057 \mathrm{kPa}$

The saturation pressure of water at $25^{\circ} \mathrm{C}=3.1698 \mathrm{kPa}$

Edited: GATE XE 2025 | Question: 56

Sun, 29 Jun 2025 16:18:26 +0000

The $\textsf{TTT}$ diagram for eutectoid steel is shown below. The steel after complete austenitization at $1073 \: \mathrm{K}$ is rapidly cooled to different temperatures and held for varying times (as indicated in $\textbf{Column I}$) followed by quenching to $300 \: \mathrm{K}$. Assuming isothermal transformation, match the heat treatment conditions in $\textbf{Column I}$ with the corresponding microstructure in $\textbf{Column II}$.

$\begin{array}{ll} \textbf{Column I} & \textbf{Column II} \\ (P) \text{Held at } 300 \mathrm{K} \text{ indefinitely} & (1) \text{Bainite} \\ (Q) \text{ Held at } 873 \mathrm{K} \text{ for } 4 \text {minutes} & (2) \text{Martensite} \\ (R) \: \text{Held at } 673 \mathrm{K} \text{ for } 20 \text{ minutes} & (3) \text{Pearlite} \\ (S) \text{Held at } 623 \mathrm{K} \text{ for } 2 \text{ minutes} & (4) \text{Bainite} + \text{Martensite} \end{array}$

$\mathrm{P}-3 ; \mathrm{Q}-2 ; \mathrm{R}-1 ; \mathrm{S}-4$
$\mathrm{P}-2 ; \mathrm{Q}-3 ; \mathrm{R}-1 ; \mathrm{S}-4$
$\mathrm{P}-2 ; \mathrm{Q}-1 ; \mathrm{R}-3 ; \mathrm{S}-4$
$\mathrm{P}-4 ; \mathrm{Q}-3 ; \mathrm{R}-1 ; \mathrm{S}-2$

Edited: GATE XE 2025 | Question: 55

Sun, 29 Jun 2025 16:17:02 +0000

The triple point $\left(T_{l}, P_{l}\right)$ is shown in a schematic phase diagram (pressure $(\mathrm{P})-$ temperature $(\mathrm{T})$ plot) for one component system. $\text{G}_s$, $\text{G}_L$ and $\text{G}_v$ are the free energies of solid, liquid and vapor, respectively. At a constant pressure, $P_{I}$, the correct free energy $(\mathrm{G})$ versus temperature $(\mathrm{T})$ plot is

Edited: GATE XE 2025 | Question: 51

Sun, 29 Jun 2025 15:57:08 +0000

If solid tin is in equilibrium with its vapor, the degree of freedom is (answer in integer) $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 47

Sun, 29 Jun 2025 13:00:06 +0000

For $\mathrm{Al}-4.5 \mathrm{wt} \% \mathrm{Cu}$ alloy, the correct sequence of precipitation during age hardening at room temperature is

GP zone $\rightarrow \theta^{\prime \prime} \rightarrow \theta^{\prime} \rightarrow \theta$
GP zone $\rightarrow \theta^{\prime} \rightarrow \theta^{\prime \prime} \rightarrow \theta$
GP zone $\rightarrow \theta^{\prime \prime} \rightarrow \theta \rightarrow \theta^{\prime}$
GP zone $\rightarrow \theta \rightarrow \theta^{\prime} \rightarrow \theta^{\prime \prime}$

Recategorized: GATE XE 2024 | Question: 34

Mon, 05 May 2025 14:39:59 +0000

The correct combination of phases in the one-component $\mathrm{H}_{2} \mathrm{O}$ phase diagram, as given below, is

$\alpha$-water; $\beta$-vapour; $\gamma$-ice
$\alpha-$ ice; $\beta-$ water; $\gamma-$ vapour
$\alpha$-vapour; $\beta$-ice; $\gamma$-water
$\alpha$-water; $\beta$-ice; $\gamma$-vapour

Recategorized: GATE XE 2024 | Question: 36

Mon, 05 May 2025 14:39:50 +0000

Differential scanning calorimetry involves measurement of

weight change
entropy
heat
vapour pressure

Recategorized: GATE XE 2024 | Question: 43

Mon, 05 May 2025 14:39:33 +0000

A binary phase diagram is given below.

Which one of the following figures qualitatively represents the $\text{G-X}$ $\text{(Gibbs free energy - composition)}$ plot at temperature $\mathrm{T}_{0}$ shown in the phase diagram?

Recategorized: GATE XE 2024 | Question: 50

Mon, 05 May 2025 14:39:09 +0000

Given that k is the first order reaction rate constant and T is the temperature in absolute scale, the temperature dependence of rate constant is/are represented by.

Recategorized: GATE XE 2022 | Question: 43

Mon, 05 May 2025 12:42:26 +0000

For a binary system at constant pressure, there are two types of invariant reactions:
(i) $\quad \alpha \leftrightarrow \beta+\gamma$
(ii) $\quad \alpha+\beta \leftrightarrow \gamma$

Analogously, how many different types of invariant reactions may exist under variable temperature and pressure, for a binary system?

Recategorized: GATE XE 2022 | Question: 44

Mon, 05 May 2025 12:42:20 +0000

For a glass marginally below its glass transition temperature, which one of the following statements is true?

Glass has higher enthalpy than both the corresponding crystalline and liquid phases
Glass has lower enthalpy than both the corresponding crystalline and liquid phases
Glass has higher entropy than the corresponding crystalline phase and lower entropy than the corresponding liquid phase
Glass has lower entropy than the corresponding crystalline phase and higher entropy than the corresponding liquid phase

Recategorized: GATE XE 2022 | Question: 47

Mon, 05 May 2025 12:42:13 +0000

During the ageing of a homogenized Al-Cu alloy $(1 \text{to} 4$ $\mathrm{wt} \% \mathrm{Cu})$ below the GP zone solvus, hardness of the alloy:

increases monotonically
decreases monotonically
first increases and then decreases
first decreases and then increases

Recategorized: GATE XE 2022 | Question: 49

Mon, 05 May 2025 12:42:02 +0000

For a diffusional transformation $\text{(i.e., growth of $\beta$ precipitates in an $\alpha$ matrix)}$, which of the following is/are true with increasing degree of undercooling?

Rate of transformation first increases and then decreases
Rate of transformation first decreases and then increases
Thermodynamic driving force increases monotonically
Mobility of atoms in $\alpha$ matrix remains unchanged

Recategorized: GATE XE 2023 | Question: 34

Mon, 05 May 2025 12:20:41 +0000

\begin{tabular}{|l|l|}
Q.44 & \begin{tabular}{l}
In age-hardening of an aluminium alloy, the purpose of solution treatment \\
followed by quenching is to
\end{tabular} \\
\hline

& form martensitic structure \\
\hline
& increase the size of the precipitates \\
\hline
& form supersaturated solid solution \\
\hline
& form precipitates at the grain boundaries \\
\hline
\end{tabular}

Recategorized: GATE XE 2023 | Question: 46

Mon, 05 May 2025 12:20:05 +0000

\begin{tabular}{|c|c|c|}
\hline Q. 56 & \multicolumn{2}{|c|}{\begin{tabular}{l}
TTT diagram of a eutectoid steel is shown below. Match the heat treatment cycle (ir \\
Column I) with its microstructure (in Column II).
\end{tabular}} \\
\hline & & \begin{tabular}{l}
Column II \\
1. Bainite only \\
2. Pearlite only \\
3. Pearlite + Bainite + Martensite \\
4. Pearlite + Martensite
\end{tabular} \\
\hline

& P-1, Q-2, R-4 & \\
\hline
& P-2, Q-3, R-2 & \\
\hline
& P-2, Q-4, R-1 & \\
\hline
& P-2, Q-3, R-1 & \\
\hline
\end{tabular}

Recategorized: GATE XE 2023 | Question: 86

Mon, 05 May 2025 12:17:57 +0000

Q. 96 Air at $400 \mathrm{~K}$ and $200 \mathrm{kPa}$ is heated at constant pressure to $600 \mathrm{~K}$. Assuming that the internal energy is a function of temperature only, the magnitude of change in internal energy during this process is $\mathrm{kJ} / \mathrm{kmol}$ (rounded off to one decimal place).
Use the following data:
Molar specific heat of air at constant volume: $\bar{c}_{v}(\mathrm{~kJ} / \mathrm{kmol}-\mathrm{K})=a+b T+c T^{2}$ where $T$ is temperature in $\mathrm{K}, a=19.686 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}, b=0.002 \mathrm{~kJ} / \mathrm{kmol}^{2}$ and $c=0.5 \times 10^{-5} \mathrm{~kJ} / \mathrm{kmol}^{3}$.

Recategorized: GATE XE 2024 | Question: 90

Mon, 05 May 2025 10:55:29 +0000

$10$ kg of water at $300$ K is poured into a bucket containing $10$ kg of water at $350$ K . Heat capacity of water is $4.2 \mathrm{~kJ} / \mathrm{kg}$. K . Neglecting any heat losses to the surroundings, the change in the entropy (in $\mathrm{kJ} / \mathrm{K}$ ) of the system during this process $\text{(rounded off to two decimal places)}$ is _________.

$0.00$
$0.25$
$0.50$
$0.75$