Propulsion Thermodynamics and Brayton Cycle - Propulsion - Aerospace Engineering Previous Year Questions

The figure below depicts two ideal gas turbine cycles, cycle 1-2-3-4-1 and cycle 1-2-3'-4'-1, on a T-s diagram. Which one the following statements is FALSE?

In an ideal turbofan engine shown in the figure below, the compressor is driven by the high pressure turbine, and the fan is driven by the low pressure turbine. The stations 0, 2, 3, 4, 4.5, and 5 refer to free-stream, compressor inlet, compressor outlet, combustor exit, high pressure turbine exit, and low pressure turbine exit, respectively, and the subscript 't' refers to the total condition. Also, \(\tau_r = T_{t0}/T_0\), \(\tau_c = T_{t3}/T_{t2}\) and \(\tau_\lambda = T_{t4}/T_0\). The total temperature ratio of the high pressure turbine (\(T_{t4.5}/T_{t4}\)) is given by ______.

Isobutane (\( C_4H_{10} \)) is burnt completely in pure oxygen as per the reaction given below. Given that the standard heats of formation (in kcal/mole) of isobutane, carbon dioxide, and water vapour are \( -31.489 \), \( -94.052 \), and \( -60.150 \), respectively, the heat of reaction is __________ kcal (rounded off to 2 decimal places).
\( C_4H_{10} + 6.5 O_2 \rightarrow 4 CO_2 + 5 H_2O \)

A furnace of 250 MW rating is used to melt and raise the temperature of aluminium from 25 °C to 900 °C. Aluminium has a solid-state specific heat, latent heat, and liquid-state specific heat of 0.9 kJ/kg·K, 390 kJ/kg, and 1.108 kJ/kg·K, respectively, and the furnace has 70% efficiency. The melting point of aluminium is 660 °C. The amount of aluminium that can be processed per hour is __________ kg (rounded off to 1 decimal place).