A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ . During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is _________ kJ (rounded off to 1 decimal place).

Specific heat of hydrogen at constant pressure $=14.56 \mathrm{~kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$

Specific heat of hydrogen at constant volume $=10.4 \mathrm{~kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$

A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains air at 140 kPa and 350 °C and the piston is resting in equilibrium at a position which is 1 m above the stops. The system is now cooled to the ambient temperature of 25 °C. Consider air to be an ideal gas with a value of gas constant $R = 0.287$ kJ/(kg·K).

The absolute value of specific work done during the process is ________ kJ/kg (rounded off to 1 decimal place)

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $$1$$) and at the end (subscript $$2$$) of the process with usual notation are:
$${P_1} = 100\,\,kPa,\,\,{V_1} = 0.2\,{m^3}$$ and $${P_2} = 200\,\,kPa,\,\,{V_2} = 0.1\,{m^3}$$
and the gas constant, $$R = 0.275$$ $$kJ/kg$$-$$K.$$ The magnitude of the work required for the process (in $$kJ$$) is _______________

A mixture of ideal gases has the following composition by mass:

If the universal gas constant is $$8314$$ $$J/kmol$$-$$K,$$ the characteristic gas constant of the mixture (in $$J/kg$$-$$K$$) is ____________.