Thermodynamics

The figure shows the velocity vectors vi and vf of a gas molecule immediately before and immediately after the molecule collides with a container wall. The force exerted by the molecule on the wall during the collision is also shown. Which of the following correctly describes the magnitude a of the acceleration of the molecule during the collision with the container wall?

A sample of gas is confined in a cylinder with a piston that moves with negligible friction. There is a block on top of the piston, and the piston is at rest. Which of the following makes a Newton’s-third-law force pair with the force that the block exerts on the piston?

• The force exerted on the piston by the gas inside the cylinder

• The gravitational force exerted on the block

• The force exerted on the block by the piston

• The force exerted on the gas inside the cylinder by the piston

Students design an experiment with a curved, insulated rod of an unknown thermally conducting material. The rod is 1 m long and 2 cm in diameter. One end of the rod is touching the surface of water kept at 350K by a hot plate, and the other end is just touching the surface of a well-insulated block of ice.

The figure shows a graph of the energy transferred by heating from the water through the rod and to the ice over time. If the temperature of the ice is held constant at 250K , what is the thermal conductivity of the rod?

• 0.03 W/(m⋅K)

• 2.5 W/(m⋅K)

• 80 W/(m⋅K)

• 314 W/(m⋅K)

Students design an experiment with a curved, insulated rod of an unknown thermally conducting material. The rod is 1 m long and 2 cm in diameter. One end of the rod is touching the surface of water kept at 350K by a hot plate, and the other end is just touching the surface of a well-insulated block of ice.

The students are required to create a procedure to determine the thermal conductivity of the rod. They first determine that they can measure the amount of ice that has melted after a given time to calculate the heat transfer over time to the block of ice. Which of the following must the students also measure to calculate the thermal conductivity of the rod?

• The mass of the rod

• The temperature of the ice

• The ambient temperature of the room

• The mass of the water

Students design an experiment with a curved, insulated rod of an unknown thermally conducting material. The rod is 1 m long and 2 cm in diameter. One end of the rod is touching the surface of water kept at 350K by a hot plate, and the other end is just touching the surface of a well-insulated block of ice.

The rod is removed from the apparatus and placed in a warm room until it reaches thermal equilibrium. Its ends are then positioned to touch the ends of an identical rod with a much colder temperature, as shown in the figure. Which of the following is the best explanation of how energy is transferred between the rods as they approach thermal equilibrium?

• Quickly moving molecules in the warm rod move into the cold rod, and slowly moving molecules in the cold rod move into the warm rod.

• Quickly vibrating molecules in the warm rod collide with slowly vibrating molecules in the cold rod, and on average the slower molecules begin to vibrate faster.

• Molecules of the warm rod collide with molecules of the cold rod, causing a net motion of molecules which results in positive work being done on the molecules of the cold rod.

• Energy cannot be transferred directly across the interface of the rods, but must first be transferred to the air molecules around the rods and then transferred back to the rods.

A gas contains two types of particles. Particle A has mass m and velocity v0 in the +z-direction. It collides head-on with particle B that has mass 5m and velocity 2v0 in the −z-direction. Electrostatic force then holds the particles together. What is the final velocity of the two-particle system?

A student conducts an experiment in which two solid rods, X and Y , are each held vertically with the bottom end just submerged in a bath of boiling water. The temperature of the room is 21°C , and the rods are each 80cm long. After each rod has been in the water for the same amount of time, the student measures the temperature at 20cm intervals along each rod. The student’s data are shown below. Which of the following correctly describes an analysis of the data that can be used to compare the thermal conductivity of the rods?

• Compare the temperatures of the rods at 0cm .

• Compare the temperatures of the rods at each height.

• Determine which rod has differences in temperatures between adjacent positions that are most similar for all pairs of positions.

• The data cannot be used to compare the thermal conductivities because the top ends of the rods are not at room temperature.

A student collects two data points for a sample of a gas that can be treated as ideal and is in a rigid container: T1=300K, P1=3.0kPa and T2=310K, P2=3.1kPa. Which of the following is the best conclusion about the pressure of an ideal gas at absolute zero (that is, T=0K) that can be made from this data?

• The pressure is 0kPa.

• No conclusion can be made, because a pattern cannot be validated based on only two data points.

• No conclusion can be made, because the substance is no longer a gas near absolute zero.

• No conclusion can be made, because the volume of the gas is zero at absolute zero, and PV=0 does not necessarily imply that pressure is zero.

Radiant floor heating systems heat the floor of a room, which transfers heat through convection currents that move warm air throughout the room. A student draws the two models shown in the figures. Which of the following best describes which model is the most accurate representation of this process?

• Figure 1, because the heat radiates away in straight-line paths from a heated point on the floor.

• Figure 1, because air near the floor is heated and expands outward from its origin.

• Figure 2, because pockets of air near the floor are heated and rise to the top of the room before cooling and falling back down to the floor.

• Figure 2, because radiation emitted by the floor circulates throughout the room.

A group of students performs an experiment to determine the thermal conductivity k of a material. They have several cylindrical rods made of the material, and the rods have different cross-sectional areas A and lengths L . They place one end of each rod in an ice bath and the other end in a hot bath and measure the rate Q/Δt of heat transfer. They plot their data with Q/Δt on the vertical axis. Which of the following quantities, when plotted on the horizontal axis, will yield a linear best-fit line from which the thermal conductivity of the material could be determined?