A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ . During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is _________ kJ (rounded off to 1 decimal place).

Specific heat of hydrogen at constant pressure $=14.56 \mathrm{~kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$

Specific heat of hydrogen at constant volume $=10.4 \mathrm{~kJ} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$

A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K . Heat loss from the auditorium is 15 kW . The power consumption of the heat pump is __________ kW (rounded off to 2 decimal places).

Consider a Pelton wheel of 1 m diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the bucket exit. The absolute speed of water at the bucket inlet is $125.66 \mathrm{~m} \mathrm{~s}-1$. For maximum power output from the Pelton wheel, the rpm of the Pelton wheel is_______ (rounded off to 1 decimal place).