A mass of $$1$$ kg is attached to two identical springs each with stiffness $$k=20kN/m$$ as shown in the figure. Under frictionless condition, the natural frequency of the system in $$Hz$$ is close to

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging diverging nozzle of exit area $$0.005{m^2}$$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is $$50$$ $$kPa.$$ The characteristic gas constant and the ratio of specific heats of air are $$0.287$$ $$kJ/kgK$$ and $$1.4$$ respectively.

The density of air in $$kg/{m^3}$$ at the nozzle exit is

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging diverging nozzle of exit area $$0.005{m^2}$$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is $$50$$ $$kPa.$$ The characteristic gas constant and the ratio of specific heats of air are $$0.287$$ $$kJ/kgK$$ and $$1.4$$ respectively.

The mass flow rate of air through the nozzle in $$kg/s$$ is

The contents of a well-insulated tank are heated by a resistor of $$23\Omega $$ in which $$10A$$ current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer to the system are positive. The rates of heat $$(Q),$$ work $$(W)$$ and change in internal energy $$\left( {\Delta U} \right)$$ during the process in $$kW$$ are