List of top Engineering Sciences Questions on Thermodynamics asked in GATE XE

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). 

A particular temperature scale is obtained according to the relation: \[ t = ae^{\alpha} + b \] where \( a \) and \( b \) are constants, and \( t \) is in \( ^\circ {C} \). The thermometric property as measured by the thermometer is \( \alpha \). The values of \( \alpha \) at the ice point and steam point are 6 and 9, respectively. The temperature (in \( ^\circ {C} \)) which gives \( \alpha = 7 \) is ........ {(rounded off to two decimal places).}
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).
Air at 101 kPa, 15°C and 50% relative humidity is first heated to 20°C in a heating coil, and then humidified by spraying water on it. In the final state, the air has temperature of 25°C and relative humidity of 85%. The amount of water sprayed (in gm per kg of dry air) is ........ (rounded off to two decimal places). Use the following data: The saturation pressure of water at 15 °C = 1.7057 kPa The saturation pressure of water at 25 °C = 3.1698 kPa
Air enters a hair dryer at \(22^\circ {C}\) and 100 kPa with a velocity of \(3.7 \, {m/s}\), and leaves the dryer at \(83^\circ {C}\) and 100 kPa with a velocity of \(9.1 \, {m/s}\). The exit area of the dryer is \(18.7 \, {cm}^2\), and the ambient temperature is \(22^\circ {C}\). The air is an ideal gas with gas constant \(R = 0.287 \, {kJ/kg-K}\) and isobaric specific heat \(c_p = 1.005 \, {kJ/kg-K}\).
If the change in potential energy is neglected, the second law efficiency (in %) of the dryer is .......... {(rounded off to one decimal place).}
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).
A stream of superheated steam (2 MPa, 300°C) mixes with another stream of superheated steam (2 MPa, 400°C) through a steady-state adiabatic process. The flow rates of the streams are 3 kg/min and 2 kg/min, respectively. This mixture then expands in an adiabatic nozzle to a saturated mixture with quality of 0.77 and 1 kPa. Neglect the velocity at the nozzle entrance and the change in potential energies. The velocity at the nozzle exit (in m/s) is ......... (rounded off to two decimal places). Use the following data:
At 2 MPa, 300 °C: Specific enthalpy of superheated steam = 3024.2 kJ/kg
At 2 MPa, 400 °C: Specific enthalpy of superheated steam = 3248.4 kJ/kg
At 1 kPa: Specific enthalpy of saturated water = 29.3 kJ/kg
At 1 kPa: Specific enthalpy of saturated vapour = 2513.7 kJ/kg
A piston-cylinder assembly having 250 mm diameter contains 0.01 kg of water vapor at 1 MPa and 200°C. The specific volume of the vapor is 0.020602 m\(^3\)/kg. The system expands as per the relation \( p v^n = {constant} \), where \( p \) is pressure and \( v \) is the specific volume. The expansion of water vapor displaces the piston by 50 mm. If the final pressure is 0.35 MPa, the value of the exponent \( n \) is ........ (rounded off to two decimal places).
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 \( R_u = 8.314 \, {kJ/kmol-K} \)
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 rigid tank of 300 litre capacity contains 3 kg of oxygen (molar mass = 32 kg/kmol) at 25°C. If oxygen behaves as an ideal gas, the pressure (in kPa) inside the tank is ......... (rounded off to two decimal places).
Use: Universal gas constant \( R_u = 8.314 \, {kJ/kmol-K} \)
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 piston-cylinder assembly having 250 mm diameter contains 0.01 kg of water vapor at 1 MPa and 200°C. The specific volume of the vapor is 0.020602 m\(^3\)/kg. The system expands as per the relation \( p v^n = {constant} \), where \( p \) is pressure and \( v \) is the specific volume. The expansion of water vapor displaces the piston by 50 mm. If the final pressure is 0.35 MPa, the value of the exponent \( n \) is ........ (rounded off to two decimal places).

A stream of superheated steam (2 MPa, 300°C) mixes with another stream of superheated steam (2 MPa, 400°C) through a steady-state adiabatic process. The flow rates of the streams are 3 kg/min and 2 kg/min, respectively. This mixture then expands in an adiabatic nozzle to a saturated mixture with quality of 0.77 and 1 kPa. Neglect the velocity at the nozzle entrance and the change in potential energies. The velocity at the nozzle exit (in m/s) is ......... (rounded off to two decimal places). 
Use the following data:
At 2 MPa, 300 °C: Specific enthalpy of superheated steam = 3024.2 kJ/kg
At 2 MPa, 400 °C: Specific enthalpy of superheated steam = 3248.4 kJ/kg
At 1 kPa: Specific enthalpy of saturated water = 29.3 kJ/kg
At 1 kPa: Specific enthalpy of saturated vapour = 2513.7 kJ/kg
 

Consider a gas obeying the relation \( P(v - b) = RT \), where \( b \) and \( R \) are constants. Which of the following statement(s) is/are CORRECT about the specific heat capacity at constant pressure?
A rigid tank of 300 litre capacity contains 3 kg of oxygen (molar mass = 32 kg/kmol) at 25°C. If oxygen behaves as an ideal gas, the pressure (in kPa) inside the tank is ......... (rounded off to two decimal places).
Use: Universal gas constant \( R_u = 8.314 \, {kJ/kmol-K} \)
If \( \gamma \) refers to the ratio of specific heats, the air-standard efficiency of an Otto cycle is
The inlet and outlet temperatures of the flowing fluid during a steady state flow process are the same as that of the surroundings. If the changes in kinetic and potential energies are neglected, the maximum power that can be obtained is equal to
A closed system undergoes a process 1–2 in which it absorbs 150 kJ of energy as heat and does 90 kJ of work. Then it follows another process 2–3 in which 80 kJ of work is done on it while it rejects 60 kJ as heat. If it is desired to restore the system to the initial state (state 1) by an adiabatic path, the work interaction (in kJ) in this process will be
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).
Air at 101 kPa, 15°C and 50% relative humidity is first heated to 20°C in a heating coil, and then humidified by spraying water on it. In the final state, the air has temperature of 25°C and relative humidity of 85%. The amount of water sprayed (in gm per kg of dry air) is ........ (rounded off to two decimal places). Use the following data: The saturation pressure of water at 15 °C = 1.7057 kPa The saturation pressure of water at 25 °C = 3.1698 kPa
Air enters a hair dryer at \(22^\circ {C}\) and 100 kPa with a velocity of \(3.7 \, {m/s}\), and leaves the dryer at \(83^\circ {C}\) and 100 kPa with a velocity of \(9.1 \, {m/s}\). The exit area of the dryer is \(18.7 \, {cm}^2\), and the ambient temperature is \(22^\circ {C}\). The air is an ideal gas with gas constant \(R = 0.287 \, {kJ/kg-K}\) and isobaric specific heat \(c_p = 1.005 \, {kJ/kg-K}\).
If the change in potential energy is neglected, the second law efficiency (in %) of the dryer is .......... {(rounded off to one decimal place).}
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).
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}