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 ____________.

$$1.5$$ $$kg$$ of water is in saturated liquid state at $$2$$ bar
$$\left( {{v_f} = 0.001061\,\,{m^3}/kg,\,\,{u_f} = 504.0kJ/kg,\,\,{h_f} = 505\,\,kJ/kg} \right).$$ 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 ________.

A mono-atomatic ideal gas $$\left( {\gamma = 1.67,} \right.$$ molecular weight$$=40$$ $$\left. \, \right)$$ is compressed adiabatically from $$0.1$$ $$MPa,$$ $$300K$$ to $$0.2$$ $$MPa.$$ The universal gas constant is $$8.314$$ $$kJ$$ $$kmo{l^{ - 1}}{K^{ - 1}}.$$ The work of compression of the gas (in $$kJ$$ $$k{g^{ - 1}}$$) is