Homework Help for Chemistry (page 6)
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In 1983, the United States began coining the one-cent piece out of copper-clad zinc rather than pure copper. The mass of the old copper penny is 3.083 g and that of the new cent is 2.517 g. The density of copper is 8.920 g/cm and that of zing is 7.133 g/cm. The new and old coins have the same volume. Calculate the percent of zinc (by volume) in the new cent.
The Otto cycle in Figure P18.64 models the operation of the internal combustion engine in an automobile. A mixture of gasoline vapor and air is drawn into a cylinder as the piston moves down during the intake stroke O → A. The piston moves up toward the closed end of the cylinder to compress the mixture adiabatically in process A → B. The ratio r = V1/V2 is the compression ratio of the engine. At B, the gasoline is ignited by the spark plug and the pressure rises rapidly as it burns in process B → C. In the power stroke C → D, the combustion products expand adiabatically as they drive the piston down. The combustion products cool further in an isovolumetric process D → A and in the exhaust stroke A → O, when the exhaust gases are pushed out of the cylinder. Assume that a single value of the specific heat ratio characterizes both the fuel-air mixture and the exhaust gases after combustion. Prove that the efficiency of the engine is .
You are working as a research assistant for a professor whose research area is thermodynamics. He points out to you that Daniel Fahrenheit used the best estimate of normal human body temperature as one of the points in defining the original Fahrenheit temperature scale. On the revised scale we now use, normal human body temperature is 98.6oF. Your professor proposes a new scale on which normal human body temperature would be exactly 100oN, where the unit oN is a degree on the New scale. The temperature of freezing water would be 0oN, as on the Celsius scale. Your professor asks you to determine the following temperatures on his new scale: (a) absolute zero, (b) the melting point of mercury (-37.9oF), (c) the boiling point of water, and, for publicity at his expected future press conference, (d) the highest recorded air temperature on the Earth's surface. 134.1oF on July 10, 1913, in Death Valley, California.
An ideal gas expands at constant pressure. (a) Show that . If the gas is monoatomic, start the definition of internal energy and show that , where is the work done by the gas on its environment. (c) For the same monoatomic ideal gas, show with the first law that . (d) Is it possible for an ideal gas to expand at constant pressure while exhausting thermal energy? Explain.
Calculate the temperature the entire sky would have to be in order to transfer energy by radiation at 1000 W/m2 - about the rate at which the Sun radiates when it is directly overhead on a clear day. This value is the effective temperature of the sky, a kind of average that takes account of the fact that the Sun occupies only a small part of the sky but is much hotter than the rest. Assume that the body receiving the energy has a temperature of 27.0oC.
One description of the potential energy of a diatomic molecule is given by the Lennard-Jones potential,
where A and B are constants and r is the separation distance between atoms. Find, in terms of A and B, (a) the value r0 at which the energy is a minimum and (b) the energy E required to break up a diatomic molecule.
A steam pipe is covered with 1.50-cm-thick insulating material of thermal conductivity 0.200 cal/cm-oC-s. How much energy is lost every second when the steam is at 200oC and the surrounding air is at 20.0oC? The pipe has a circumference of 800 cm and a length of 50.0 m. Neglect losses through the ends of the pipe.
A sphygmomanometer is a device used to measure blood pressure, typically consisting of an inflatable cuff and a manometer used to measure air pressure in the cuff. In a mercury sphygmomanometer, blood pressure is related to the difference in heights between two columns of mercury.
The mercury sphygmomanometer shown in Figure P9.15 contains air at the cuff pressure P. The difference in mercury heights between the left tube and the right tube is h = 115 mmHg = 0.115 m, a normal systolic reading. What is the gauge systolic blood pressure Pgauge in Pascals? The density of mercury is and the ambient pressure is .
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