Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• (a) Write an expression for the total energy Etot of a mole of a monatomic gas at temperature T. (See Problem 1.) (b) Use this to find the (constant-volume) molar specific heat Cv of the gas. This is the energy needed to raise the temperature of 1 mol by 1 K, so is equal to dEtot/dT.
Problem 1
•• (a) What is the total energy Etot of a mole of helium gas at room temperature, T ≈ 293 K? [Hint: This is just N〈K〉, where N is the number of atoms and 〈K〉 is the average kinetic energy per atom.] (b) By how many kelvins would this energy raise the temperature of a cup of water (200 grams, say)?
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