List of top Thermodynamics Questions asked in GATE XE

A cylinder of volume 1 m\(^3\) contains a mixture of CO\(_2\) (20% by mol) and O\(_2\) (80% by mol) at 100 kPa and 300 K. This cylinder is connected to a 1 MPa pressure line carrying N\(_2\) at 300 K. The cylinder is filled isothermally till the pressure of gas mixture inside it becomes 500 kPa, and then the filling is stopped. The amount of N\(_2\) gas that has entered the cylinder is \(\underline{\hspace{2cm}}\) (in mole, 2 decimal places). 
The universal gas constant is 8.3145 J/(mol K).

Two identical pressure cookers, Cooker A and Cooker B, each having a total internal capacity of 6 litres are available. Cooker A is filled with 2 litres of liquid water at 110°C and Cooker B is filled with 4 litres of liquid water at 110°C. The remaining space in both the cookers is filled with saturated water vapour in equilibrium with the liquid water. If \( g \) represents the specific Gibbs free energy, and subscripts \( v \) and \( l \) represent the saturated vapour and the saturated liquid phases, respectively, which of the following expressions is correct? 
 

Four different Entropy (S) - Temperature (T) diagrams, representing liquid to vapour phase transition process of a pure substance in a closed system under constant pressure are shown. The diagram, which correctly represents the process, is: 
 

Air having a mass flow rate of 2 kg/s enters a diffuser at 100 kPa and 30°C, with a velocity of 200 m/s. Exit area of the diffuser is 400 cm2 while the exit temperature of the air is 45°C. The rate of heat loss from the diffuser to the surrounding is 8 kJ/s. The pressure at the diffuser exit is \(\underline{\hspace{2cm}}\) kPa (2 decimal places).

For the Refrigerant R-134 (at 1 MPa and 50°C), the difference between the specific volume computed by assuming it to be an ideal gas and its actual specific volume is: \( v_{\text{ideal}} - v_{\text{actual}} = 4.529 \times 10^{-3} \, \text{m}^3/\text{kg} \). If the compressibility factor associated with this state is \( Z = 0.84 \), then \( v_{\text{com}} - v_{\text{actual}} = \underline{\hspace{2cm}} \times 10^{-3} \, \text{m}^3/\text{kg} \) (3 decimal places).

Air at a pressure of 1 MPa and 300 K is flowing in a pipe. An insulated evacuated rigid tank is connected to this pipe through an insulated valve. The volume of the tank is 1 m3. The valve is opened and the tank is filled with air until the pressure in the tank is 1 MPa. Subsequently, the valve is closed. Consider air to be an ideal gas and neglect bulk kinetic and potential energy. The final temperature of air in the tank is \(\underline{\hspace{2cm}}\) K (1 decimal place).

A cylinder of volume 0.1 m3 is filled with 100 mol of propane (C3H8) at 2 MPa. If propane is assumed to obey the van der Waals equation of state, then its temperature is \(\underline{\hspace{2cm}}\) K (1 decimal place).

A 0.8 m3 insulated rigid tank contains 1.5 kg of an ideal gas at 100 kPa. Electric work is done on the system until the pressure in the tank rises to 135 kPa. The loss in availability (exergy) associated with the process is \(\underline{\hspace{2cm}}\) kJ (2 decimal places).

An air-standard Diesel cycle with a compression ratio of 16 takes air at 1 bar and 300 K. If the maximum temperature in the cycle is 2100 K, then the thermal efficiency of the cycle is \(\underline{\hspace{2cm}}\) % (1 decimal place). 
The ratio of the specific heat capacities of air is 1.4.

A mixture of air and water vapour enters a steady-flow adiabatic saturator at 50°C and 100 kPa. It leaves the saturator in a completely saturated state at temperature 25°C and pressure of 100 kPa. Liquid water enters the saturator at 25°C. If air is considered to be an ideal gas, with constant specific heat capacity, the relative humidity of the air entering the saturator is \(\underline{\hspace{2cm}}\) % (1 decimal place).
A frictionless piston cylinder device contains 1 kg of an ideal gas. The gas is compressed according to \( P v^{1.3} = \text{constant} \) (P is pressure and v is mass specific volume), from 100 kPa, 250 K, till it reaches a temperature of 500 K. The heat transfer from the piston cylinder device to its surroundings is \(\underline{\hspace{2cm}}\) kJ (2 decimal places).
A rigid tank contains 1.0 kg of pure water consisting of liquid and vapour phases in equilibrium at 10 bar. If the liquid and vapour phase each occupies one half of the volume of the tank, then the net enthalpy of the contents of the tank is \(\underline{\hspace{2cm}}\) kJ (1 decimal place).
For a refrigeration cycle, the ratio of actual COP to the COP of a reversible refrigerator operating between the same temperature limits is 0.8. The condenser and evaporator temperatures are \(51^\circ C\) and \(-30^\circ C\), respectively. If the cooling capacity of the plant is 2.4 kW, then the power input to the refrigerator is:
The saturation pressure \(P_{\text{sat}}\) of a pure liquid is represented by an equation of the form: \[ \ln P_{\text{sat}} = A - \frac{B}{T}, \] where \(A\) and \(B\) are constants, and \(T\) is the absolute temperature. For this substance, which of the following expression for the specific entropy difference between the saturated vapour and the saturated liquid phase \((s_{fg})\) is correct?
Atmospheric air with Dry Bulb Temperature (DBT) of 24°C and Relative Humidity of 35%, entering in a circular duct (assume no pressure drop in the duct) is heated by an electrical resistance arrangement inside the duct. The DBT of air measured at the outlet of the duct is equal to 30°C. Considering the flow to be steady, which of the following statement(s) is (are) correct as regards to the outlet air, with respect to the inlet air?
Two air streams of mass flow rates \( \dot{m_1} \) and \( \dot{m_2} \) enter a mixing chamber and exit after perfect mixing. The corresponding temperatures of the inlet streams are \( T_1 \) and \( T_2 \), respectively. Heat loss rate from the mixing chamber to the surrounding is \( \dot{Q} \). Assume that the process is steady, specific heat capacity is constant, and air behaves as an ideal gas. Identify the correct expression for the final exit temperature \( T_3 \) after mixing. The mass specific heat capacities of the gas at constant volume and constant pressure are \( c_v \) and \( c_p \), respectively. Neglect the bulk kinetic and potential energies of the streams.
For a real gas passing through an insulated throttling valve, the outlet temperature of the gas \(\underline{\hspace{2cm}}\) with respect to the inlet temperature.
A closed system consists of a solution of liquid water and ethanol in equilibrium with its vapours. Using the Gibbs phase rule, the degree of freedom of the system is:
A refrigerator working on a reversed Carnot cycle has a Coefficient of Performance (COP) of 4. If it works as a heat pump and consumes work input of 1 kW, the heating effect will be:
The liquid phase of a pure substance is termed as \(\underline{\hspace{2cm}}\), if its temperature is lower than the saturation temperature corresponding to its pressure \(P\).