Assuming Earth to be a black sphere with a surface temperature of 300 K at top of the atmosphere, what must Earth's internal heat generation be in order to maintain that temperature? (neglect radiation from the stars, but not the sun)

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.2-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kpa (gage) in the tank. if the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top in liters per second.