For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?

An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?

An aluminum rod 0.500 m in length and with a cross-sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 300 K. (a) If one-half of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool. (b) If the circular surface of the upper end of the rod is maintained at 300 K, what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 W/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)

In a common demonstration, a bottle is heated and stoppered with a hard-boiled egg that's a little bigger than the bottle's neck. When the bottle is cooled, the pressure difference between inside and outside forces the egg into the bottle. Suppose the bottle has a volume of 0.500 L and the temperature inside it is raised to 80.0 while the pressure remains constant at 1.00 atm because the bottle is open. (a) How many moles of air are inside? (b) Now the egg is put in place, sealing the bottle. What is the gauge pressure inside after the air cools back to the ambient temperature of 25 but before the egg is forced into the bottle ?

Most cars have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at 10.0 . What volume of radiator fluid will overflow when the radiator and fluid reach a temperature of 95.0 , given that the fluid's volume coefficient of expansion is =400106/C? (Your answer will be a conservative estimate, as most car radiators have operating temperatures greater than 95.0 ).

Consider the latent heat of fusion and the latent heat of vaporization for H2O, 3.33 105 J/kg and 2.256 106 J/kg, respectively. How much heat is needed to a. melt 2.00 kg of ice and b. vaporize 2.00 kg of water? Assume the temperatures of the ice and steam are at the melting point and vaporization point, respectively. (a). UsingEq21.9, Q = mLF = (2.00 kg) (3.33l05 J/kg) = 6.66105 J (b).UsingEq21.10. Q = mLV = (2.00kg) (2.256106 J/kg) = 14.51106 J

A firewalker runs across a bed of hot coals without sustaining burns. Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a 3.00-mm-thick callus with a conductivity at the low end of the range for wood and its density is 300 kg/m3. The area of contact is 25.0 cm2 the temperature of the coals is 700 , and the time in contact is 1.00 s. Ignore the evaporative cooling of sweat.

An aluminum rod 0.500 m in length and with a cross sectional area of 2.50 cm2 is inserted into a thermally insulated vessel containing liquid helium at 4.20 K. The rod is initially at 3(H) K. (a) If one-halt of the rod is inserted into the helium, how many liters of helium boil off by the time the inserted half cools to 4.20 K? Assume the upper half does not yet cool, (b) If the circular surface of the upper end of the rod is maintained at 300 K. what is the approximate boil-off rate of liquid helium in liters per second after the lower half has reached 4.20 K? (Aluminum has thermal conductivity of 3 100 YV/m K at 4.20 K; ignore its temperature variation. The density of liquid helium is 125 kg/m3.)

Consider the Maxwell-Boltzmann distribution function plotted in Problem 28. For those parameters, determine the rms velocity and the most probable speed, as well as the values of f(v) for each of these values. Compare these values with the graph in Problem 28. 28. Plot the Maxwell-Boltzmann distribution function for a gas composed of nitrogen molecules (N2) at a temperature of 295 K. Identify the points on the curve that have a value of half the maximum value. Estimate these speeds, which represent the range of speeds most of the molecules are likely to have. The mass of a nitrogen molecule is 4.68 1026 kg. Equation 20.18 can be used to find the rms velocity given the temperature, Boltzmanns constant, and the mass of the atom or molecule. The mass of a nitrogen molecule is 4.68 1026 kg. vrms=3kBTm=3(1.381023J/K)4.681026kg=511m/s Using the results of Problem 28 and the rms velocity, we can calculate the value of f(v). f(vrms) = (3.11 108)(511)2 e(5.75106(511)2) = 0.00181 The most probable speed, for which this function has its maximum value, is given by Equation 20.20. vmp=2kBTm=2(1.381023J/K)(295K)4.681026kg=417m/s f(vmp) = (3.11108)(417)2 e(5.75106(417)2) = 0.00199 We plot these points on the speed distribution. The most probable speed is indeed at the peak of the distribution function. Since the function is not symmetric, the rms velocity is somewhat higher than the most probable speed. Figure P20.29ANS