Final answer:
When case temperature is maintained and volume for vapor is created in a syringe with liquid ether, the vapor pressure would approximate the substance's saturated vapor pressure at that temperature. High altitude affects cooking times because lower atmospheric pressure lowers the boiling point of water. Increases in temperature raise pressure within an aerosol can, which is why safety warnings are issued against high storage temperatures or incineration.
Step-by-step explanation:
When a syringe containing liquid ether at a temperature of 20 °C is manipulated to create a space for vapor without changing the temperature, the resulting vapor pressure is determined by the characteristics of the ether. At a constant temperature, the vapor pressure would be approximately equal to the saturated vapor pressure of ether at that temperature. The saturated vapor pressure is a fixed property for any given substance at a particular temperature and can be found in thermodynamic tables or a chemical handbook.
The observation that it takes longer to cook an egg at high altitudes, such as in Ft. Davis, Texas, can be explained by changes in atmospheric pressure. At higher altitudes, the atmospheric pressure is lower, and consequently, water boils at a lower temperature. Because the boiling point of water is lower, cooking food by boiling takes longer since the temperature of the boiling water isn't as high as it would be at sea level.
Regarding safety warnings on a can, storing aerosols below a certain temperature is crucial because high temperatures can increase the pressure inside the can. Using the Ideal Gas Law, we find that if a can with gas at 24 °C and 360 kPa is heated to 50 °C, the pressure will increase, assuming the volume doesn't change. The higher the temperature, the greater the pressure, and if it rises enough, it could cause the can to burst or explode, hence the warning not to store at high temperatures or incinerate.
An ideal heat pump with a coefficient of performance of 12.0, used to heat an environment at 22.0°C, requires a cold reservoir temperature. The coefficient of performance (COP) for a heat pump is defined as the heat removed from the warm environment for each energy unit of work put into the system. The cold reservoir temperature can be calculated using the COP and the temperature of the heated environment.
The coefficient of performance for a heat pump is also influenced by the temperatures of the heat source and sink. For a heat pump working between 5.00°C and 35.0°C, the best possible COP can be calculated based on the temperatures of the two environments. Notice that such coefficients are approximate values and might vary according to actual operating conditions.
A thermodynamic engine operating cyclically between two reservoirs with temperatures 600 K and 300 K absorbs heat from the higher temperature and discards heat to the lower temperature one. The efficiency of such an engine can be determined by the Carnot efficiency formula, which is a function of the temperatures of the heat reservoirs.