List of top Thermodynamics Questions on First law of Thermodynamic asked in GATE XE

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).

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 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).
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.