List of top Questions asked in GATE Engineering Sciences

Two Carnot heat engines (E1 and E2) are operating in series as shown in the figure. Engine E1 receives heat from a reservoir at \(T_H = 1600 \, {K}\) and does work \(W_1\). Engine E2 receives heat from an intermediate reservoir at \(T\), does work \(W_2\), and rejects heat to a reservoir at \(T_L = 400 \, {K}\). Both the engines have identical thermal efficiencies. The temperature \(T\) (in K) of the intermediate reservoir is ........ (answer in integer). \begin{center} \includegraphics[width=5cm]{107.png} \end{center}

Air in an ideal Diesel cycle is compressed from 3 litre to 0.15 litre. It then expands during a constant pressure heat addition process to 0.3 litre. If the ratio of specific heats, \( \gamma = 1.4 \), the thermal efficiency (in %) of the cycle is ........ (rounded to one decimal place).

In a piston cylinder assembly, one kmol of an ideal gas is compressed from an initial state of 200 kPa and 400 K to a final state of 1 MPa and 400 K. If the surroundings are at 400 K, the minimum amount of work (in kJ/kmol) required for the compression process is .............{(rounded off to two decimal places).}
Use: Universal gas constant \( R_u = 8.314 \, {kJ/kmol·K} \)

A steam boiler contains saturated water vapour at 200°C. After a certain period, the temperature of the boiler drops to 110°C. Assume that all the valves of the boiler are closed and the energy is lost as heat to the surroundings. The ratio of mass of liquid to the mass of vapour is ........... (rounded off to two decimal places).

A heat engine having thermal efficiency of 40% receives heat from a source at 600 K and rejects heat to a sink at 300 K. The second-law efficiency (in %) of this engine is ......... (answer in integer).

A tank of 4 m\(^3\) contains an ideal gas mixture of 60% hydrogen and 40% nitrogen by volume at 100 kPa and 300 K. Nitrogen is added to the tank such that the composition changes to 50% nitrogen by volume, with a final temperature of 300 K. The amount of nitrogen (in kmol) to be added is ........ (rounded off to three decimal places).
Use: Universal gas constant \( R_u = 8.314 \, {kJ/kmol-K} \)

For a pure substance that expands on freezing, which of the following statement(s) is/are CORRECT?

For an ideal gas turbine cycle, \( T_1 \) and \( T_3 \) are the compressor inlet temperature and turbine inlet temperature respectively. The ratio \( \frac{T_3}{T_1} \) is denoted by \( t \) and the ratio of specific heats is denoted by \( \gamma \). For any given \( t \), the optimum pressure ratio for the maximum specific work output is

A piston-cylinder arrangement contains an ideal gas mixture of 4 kg of hydrogen and 13 kg of nitrogen at 250 K and atmospheric pressure. On heat addition, the mixture expands at constant pressure until the temperature rises to 350 K. The average isobaric specific heats \( c_p \) for hydrogen and nitrogen are 14.239 kJ/kg-K and 1.040 kJ/kg-K, respectively. The amount of heat (in MJ) added to the cylinder is ......... (rounded off to three decimal places).

A tank is divided into two compartments with one compartment containing a gas at a given pressure, while the second is completely evacuated. If the partition is removed, the gas occupies the entire compartment. Which one of the following statements is CORRECT?

A cylinder of volume \( 0.1 \, {m}^3 \) is filled with nitrogen at 10 MPa and 300 K. Consider nitrogen to be an ideal gas. The cylinder develops a leak and nitrogen escapes to atmosphere which is at 0.1 MPa. After some time, the pressure in the cylinder reduces to 5 MPa. Assuming the cylinder and the leaked gas temperature remains constant at 300 K, the work done (in MJ) by nitrogen gas is

Let \( T_H \) and \( T_L \) denote the absolute temperatures of high and low temperature reservoirs, respectively. The coefficient of performance of a reversible refrigerator operating between these two reservoirs is

A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column’s section modulus, \( EI \), is \( 9.82 \times 10^5 \, {Nm}^2 \) and the cross-section area is \( 7.85 \times 10^{-3} \, {m}^2 \). The length of the column is 2 m. The yield stress of the material is 145 MPa.
If the column can fail either in buckling or by Tresca’s criterion, the maximum load that the structure can safely sustain is ............ kN (rounded off to one decimal place).

Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?

At 873 K, hydrogen diffuses under steady state condition through a 5 mm thick palladium sheet with a cross-sectional area of 0.3 m\(^2\). The concentrations of hydrogen at high and low pressure ends of the sheet are 3 kg/m\(^3\) and 0.5 kg/m\(^3\), respectively. The amount of hydrogen (in kg per day) passing through the sheet is (rounded off to two decimal places) ............
Given: At 873 K, diffusivity of hydrogen $= 1.8 \times 10^{-8}\ {m}^2 \cdot {s}^{-1}$

The standard free energy change for the reaction, \( {SO}_2 + \frac{1}{2} {O}_2 \rightleftharpoons {SO}_3 \) at equilibrium is given by \( \Delta G^\circ = -94600 + 89.37T \), where \( T \) is in Kelvin and \( \Delta G^\circ \) is in Joules. The equilibrium constant (\( K_p \)) at 1050 K is (rounded off to two decimal places) ...........
Given: Universal gas constant (R) $= 8.314\ {J} \cdot {K}^{-1} \cdot {mol}^{-1}$

A GaP–GaAs semiconductor LED display has a band gap of 1.9 eV. The wavelength of emitted light in \( \mu \)m is (rounded off to two decimal places) .........

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

For a conventional optical microscope, which of the following options regarding the resolution limit and the depth of field is/are correct?

For Al – 4.5 wt% Cu alloy, the correct sequence of precipitation during age hardening at room temperature is:

B is the magnetic flux density and \( T_c \) is the critical temperature. The Meissner effect is represented by:

Which of the following phenomenon/phenomena contribute to intensity loss of electromagnetic radiation during transmission through a medium?