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By the conditions of the problem, we have or which gives Substituting Eq. 6 into Eq. 1 yields

One mole of Ar atoms are confined in a vessel whose volume is 1,000cm3. If all of the atoms are moving with identical speeds of 230 m/s in the x, y and z directions, compute the expected pressure, in kPa , inside the vessel. What is the pressure in atm.

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By the conditions of the problem, we have or which gives Substituting Eq. 6 into Eq. 1 yields

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  1. Onemole of Ar atoms are confined in a vessel whose volume is 1,000cm3. If all of the atoms are moving with identical speeds of 230 m/s in the x, y and z directions, compute the expected pressure, in kPa, inside the vessel. What is the pressure in atm. A right circular cylinder whose radius is 1 cm contains a mixture of Hg (d = 13.596 kg/L) and H2O (d = 1.000 kg/L), with the mercury on the bottom of the cylinder and the water on the top. It is found that the pressure at the bottom of the cylinder is 1.200 atm. It is also determined that the mass of Hg in the cylinder is eight times the mass of water present. Determine the length of the Hg column, hm, and the length of the water column , hw, in the cylinder. (Be careful with the units)

  2. It is found that the lengths of two metal rods, denoted A and B, are linear functions of the absolute temperature T. That is, where A0 is the length of rod A at T=0 K and a1is a positive constant, and with similar definitions for b0 and b1. An investigator now defines two temperature scales based on the lengths of rods A and B, respectively. The temperature tA and tB aredefined by and where L0 and L100 are the lengths of the rod at the normal freezing and boiling points, respectively. (A) Determine the relationship between tA and T. (B) Show that tA = tB at all values of T, even if a0 ≠ b0 and a1 ≠ b1.

  3. Onemole of Ar atoms are confined in a vessel whose volume is 1,000cm3. If all of the atoms are moving with identical speeds of 230 m/s in the x, y and z directions, compute the expected pressure, in kPa, inside the vessel. What is the pressure in atm. Sol) Eq 1.4 show that Or in atm, we have

  4. A right circular cylinder whose radius is 1 cm contains a mixture of Hg (d = 13.596 kg/L) and H2O (d = 1.000 kg/L), with the mercury on the bottom of the cylinder and the water on the top. It is found that the pressure at the bottom of the cylinder is 1.200 atm. It is also determined that the mass of Hg in the cylinder is eight times the mass of water present. Determine the length of the Hg column, hm, and the length of the water column , hw, in the cylinder. (Be careful with the units) Sol) The total pressure at the bottom of the cylinder is that exerted by the Hg plus that produced by the H2O. That is, Since the volume of a right circular cylinder is given by , we have And for the water,

  5. By the conditions of the problem, we have or which gives Substituting Eq. 6 into Eq. 1 yields so that we have

  6. Converting all units to the SI system, we obtain

  7. It is found that the lengths of two metal rods, denoted A and B, are linear functions of the absolute temperature T. That is, where A0 is the length of rod A at T=0 K and a1 is a positive constant, and with similar definitions for b0 and b1. An investigator now defines two temperature scales based on the lengths of rods A and B, respectively. The temperature tA and tB aredefined by and where L0 and L100 are the lengths of the rod at the normal freezing and boiling points, respectively. (A) Determine the relationship between tA and T. (B) Show that tA = tB at all values of T, even if a0 ≠ b0 and a1 ≠ b1.

  8. (A) Direct substitution of the dependence of upon T into the definition of gives which is the required relationship between and T. In deriving the result, we have made use of the fact that and for the normal freezing and boiling points of H2O, respectively. (B) Proceeding in the same manner for the temperature scale , we obtain

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