List of top Thermodynamics Questions asked in GATE Engineering Sciences

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).

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: - Saturation pressure of water at 15°C = 1.7057 kPa - Saturation pressure of water at 25°C = 3.1698 kPa

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). Data given: - At 2 MPa, 300 °C: \(h = 3024.2 \, \text{kJ/kg}\) - At 2 MPa, 400 °C: \(h = 3248.4 \, \text{kJ/kg}\) - At 1 kPa: \(h_f = 29.3 \, \text{kJ/kg}, h_{fg} = 2513.7 \, \text{kJ/kg}\)

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 0.20602 m³/kg. The system expands as per the relation \(pV^n = \text{constant}\), where \(n\) is the polytropic exponent. The expansion of water vapour 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).

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

If \(\gamma\) refers to the ratio of specific heats, the air-standard efficiency of an Otto cycle is

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: \(R_u = 8.314 \, kJ/kmol-K\)

For an ideal gas turbine cycle, \(T_1\) and \(T_3\) are the compressor inlet temperature and turbine inlet temperature respectively. The ratio \(\dfrac{T_3}{T_1}\) 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 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?

The standard free energy change for the reaction \[ SO_2 + \tfrac{1}{2}O_2 \rightleftharpoons SO_3 \] is given by \(\Delta G^\circ = -94600 + 89.37T\) (J). At \(T=1050\,K\), the equilibrium constant \(K_p\) is (rounded off to two decimal places). Given: Universal gas constant \(R=8.314\,J\,mol^{-1}K^{-1}\).

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

The triple point \((T_t, P_t)\) is shown in a schematic phase diagram (pressure (P) – temperature (T) plot) for a one–component system. \(G_S, G_L\) and \(G_V\) are the free energies of solid, liquid, and vapor, respectively. At a constant pressure, \(P_t\), the correct free energy (G) versus temperature (T) plot is: