The natural frequency of the system shown below is

Water has a critical specific volume of $$0.003155$$ $${m^3}/kg.$$ A closed and rigid steel tank of volume $$0.025{m^3}$$ contains a mixture of water and steam at $$0.1MPa.$$ The mass of the mixture is $$10$$ $$kg.$$ The tank is now slowly heated. The liquid level inside the tank.

A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a high temperature reservoir while rejecting the remaining part to a low temperature heat sink. In such a heat transformer, $$100kJ$$ of heat is supplied at $$350$$ $$K.$$ The maximum amount of heat in $$kJ$$ that can be transferred to $$400K,$$ when the rest is rejected to a heat sink at $$300K$$ is

An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a sink at a rate of $$50kW.$$ The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at $${17^ \circ }C$$ and $${75^ \circ }C$$. The rate (in $$kW$$) at which the heat pump delivers heat to its high temperature sink is