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Chapter 9: Problem 1270

At \(0 \mathrm{~K}\) which of the following properties of a gas will be zero (A) Kinetic energy (B) Density (C) Potential energy (D) Vibrational energy

Short Answer

Expert verified
At 0 K, the kinetic energy of a gas will be zero (Option A), as the motion of the gas particles is minimized or stopped. The other properties, such as density, potential energy, and vibrational energy, will still have nonzero values.

Step by step solution

01

Analyzing Kinetic Energy

The Kinetic energy of the gas is a measure of the motion of the gas particles. At 0 K, the motion of the gas particles is minimized or stopped, depending on the type of kinetic energy. The kinetic energy for an ideal gas is given by the equation: \( KE = \frac{3}{2}nRT \) where KE is kinetic energy, n is the number of moles, R is the gas constant, and T is the temperature (in Kelvin). At 0 K, the temperature term becomes zero, and thus, the kinetic energy of the gas will also be zero.
02

Analyzing Density

Density is defined as mass per unit volume. At 0 K, the gas particles will still have mass and occupy space, so the density will not be zero.
03

Analyzing Potential Energy

Potential energy is the energy a system possesses due to the position of its particles and the forces acting on those particles (such as due to gravity). At 0 K, these forces won't necessarily be zero, and the potential energy will still exist.
04

: Analyzing Vibrational Energy

: The vibrational energy of a gas is related to the energy stored in the vibrations between atoms in a molecule. At absolute zero, a molecule's vibrational modes are in its lowest possible energy state, called the ground state. However, the vibrational energy is not necessarily zero at 0 K, due to the zero-point energy phenomenon. In conclusion, At 0 K, only the kinetic energy of a gas will be zero (Option A). The other properties will still have nonzero values.

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Most popular questions from this chapter

1 mole of gas occupies a volume of \(100 \mathrm{~m} 1\) at \(50 \mathrm{~mm}\) pressure. What is the volume occupied by two moles of gas at $100 \mathrm{~mm}$ pressure and at same temperature (A) \(50 \mathrm{ml}\) (B) \(200 \mathrm{ml}\) (C) \(100 \mathrm{ml}\) (D) \(500 \mathrm{~m} 1\)

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The root mean square speed of hydrogen molecules of an ideal hydrogen kept in a gas chamber at \(0^{\circ} \mathrm{C}\) is \(3180 \mathrm{~ms}^{-1}\). The pressure on the hydrogen gas is (Density of hydrogen gas is $8.99 \times 10^{-2} \mathrm{~kg} / \mathrm{m}^{3}, 1 \mathrm{~atm}=1.01 \times 10^{5} \mathrm{Nm}^{-2}$ ) (A) \(1.0 \mathrm{~atm}\) (B) \(3.0 \mathrm{~atm}\) (C) \(2.0 \mathrm{~atm}\) (D) \(1.5 \mathrm{~atm}\)

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