The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is $$2.87{m^3}$$ and $$300$$ $$K,$$ respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is $$0.5$$ bar. If the gas constant of air is
$$R =287J/kgK$$ and the atmospheric pressure is $$1$$ bar, the mass of air (in $$kg$$) in the vessel is

A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $$1100K$$ and $$400K.$$ respectively. The power produced is $$4.6MW$$ and heat escapes at the rate of $$300kJ/s$$ through the turbine casing. The mass flow rate of the gas (in $$kg/s$$) through the turbine is.

A mass $$m$$ of a perfect gas at pressure $${p_1}$$ and volume $${V_1}$$ undergoes an isothermal process. The final pressure is $${p_2}$$ and volume is $${V_2}.$$ The work done on the system is considered positive. If $$R$$ is the gas constant and $$T$$ is the temperature, then the work done in the process is

One $$kg$$ of an ideal gas (gas constant $$R=287$$ $$J/kg$$-$$K$$) undergoes an irreversible process from state- $${\rm I}$$ ( $$1$$ bar, $$300$$ $$K$$ ) to state-$$2$$ ( $$2$$ bar, $$300$$ $$K$$). The change in specific entropy $$\left( {{s_2} - {s_1}} \right)$$ of the gas (in $$J/kg$$.$$K$$) in the process is ____________