A heat pump extracts 7.0 × 10^6 J of heat per hour from a well at 280 K and delivers its output heat into a house at 320 K. If the heat pump uses an ideal Carnot cycle in its operation, what minimum work must be supplied to the heat pump per hour?

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?