Calculation of Work and Heat · Thermodynamics · GATE ME
Marks 1
$$(i)$$ They are boundary phenomena
$$(ii)$$ They are exact differentials
$$(iii)$$ They are path functions
$$v=$$ specific volume and $$P=$$ pressure of the gas.
The specific work required to be supplied to the compressor for this gas compression process is
Marks 2
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)

$${P_1} = 100\,\,kPa,\,\,{V_1} = 0.2\,{m^3}$$ 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 _______________

If the universal gas constant is $$8314$$ $$J/kmol$$-$$K,$$ the characteristic gas constant of the mixture (in $$J/kg$$-$$K$$) is ____________.
$$\left( {{v_f} = 0.001061\,\,{m^3}/kg,\,\,{u_f} = 504.0kJ/kg,\,\,{h_f} = 505\,\,kJ/kg} \right).$$ Heat is added in a constant pressure process till the temperature of water reaches
$${400^ \circ }C\left( {v = 1.5493{m^3}/kg,u = 2967.0\,kJ/kg,\,\,h = 3277.0\,kJ/kg} \right).$$ The heat added (in $$kJ$$) in the process is ________.
Find the rise in temperature of air.
