A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was $${5^ \circ }C$$.
Assume that the volume of the football remains constant at $$2500c{m^3}$$

Gauge pressure of air to which the ball must have been originally inflated so that it would equal $$1$$ bar gauge at the stadium is

A $$100$$ $$W$$ electric bulb was switched on in a $$2.5\,m \times 3m \times 3m$$ size thermally insulated room having a temperature of $${20^ \circ }C$$. The room temperature at the end of $$24$$ hours will be

Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$

Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed water heating improves the efficiency of the steam turbine.

Reason(R): The regenerative feed water heating raises the average temperature of heat addition in the Rankine cycle.

Assertion (A): Condenser is an essential equipment in a steam power plant.

Reason(R): For the same mass flow rate and the same pressure rise, a water pump requires substantially less power than a steam compressor.