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

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.

Match the items in columns $$I$$ and $$II$$.

Column $$I$$
$$P:$$ Centrifugal compressor
$$Q:$$ Centrifugal pump
$$R:$$ Pelton wheel
$$S:$$ Kaplan turbine

Column $$II$$
$$1:$$ Axial flow
$$2:$$ Surging
$$3:$$ Priming
$$4:$$ Pure impulse

A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If $$N$$ is the $$RPM$$ of the full scale turbine, then the $$RPM$$ of the model will be