13/14 MisConceptual Questions
Two beakers contain a mixture of ice and water at equilibrium. Beaker A has less ice than Beaker B. Which beaker is the coldest, or are they equal in temperature? (a) Beaker A (b) Beaker B (c) Equal
Answer: c) Equal Students frequently interpret having more ice with being colder. However, whenever ice and water are mixed together and are in thermal equilibrium they will be at the melting/freezing point of the water. Therefore, the two containers will be at the same temperature.
When using the ideal gas law, which of the following rules must be obeyed? (a) Always use temperature in kelvins and absolute pressure. (b) Always use volume in m^3 and temperature in kelvins. (c) Always use gauge pressure and temperature in degrees Celsius. (d) Always use gauge pressure and temperature in kelvins. (e) Always use volume in m^3 and gauge pressure
Answer:(a) Always use temperature in kelvins and absolute pressure. Students frequently do not understand that gauge pressure and temperature in Celsius are a comparison of pressure and temperature to an arbitrary zero point. For the ideal gas law to hold, the temperature, pressure, and volume must be measured relative to the true zero points: absolute zero pressure, absolute zero temperature, and zero volume. The volume units are not critical, since changing them only affects the value of the ideal gas constant. Gauge pressure and Celsius temperature have additive terms that change the functional form of the ideal gas law.
Two identical bottles at the same temperature contain the same gas. If bottle B has twice the volume and contains half the numbers of moles of gas as bottle A, how does the pressure in B compare with the pressure in A?
By the ideal gas law, when the temperature is held constant, the pressure is proportional to the number of moles and inversely proportional to the volume. If the second bottle has twice the volume with only half the number of moles, it would only experience one-fourth the pressure.
In a mixture of gases oxygen and helium, which statement is valid? (a) The helium atoms will be moving faster than the oxygen molecules, on average. (b) both will be moving at the same speed (c) the oxygen molecules will, on average be moving more rapidly than the helium atoms (d) the kinetic energy of helium atoms will exceed that of oxygen molecules (e) None of the above
answer: (a) The helium atoms will be moving faster than the oxygen molecules, on average. In the mixture, the oxygen molecules and helium atoms will be at the same temperature, which means that their average molecular kinetic energies will be the same. Since a helium atom has less mass than an oxygen molecule, the helium atoms will be moving faster than the oxygen molecules on average.
For objects at thermal equilibrium, which of the following is true? (a) Each is at the same temperature. (b) Each has the same internal energy (c) Each has the same heat (d) All of the above (e) None of the above
answer: (a) each is at the same temperature When two objects are in thermal equilibrium, heat does not transfer between them. This occurs when the two objects are at the same temperature. Internal energy is an extrinsic property that depends upon the amount of the substance present. Therefore, two gases in thermal equilibrium with each other would have different internal energies if one consisted of one mole of gas and the other consisted of two moles of gas. Heat is a transfer of energy between objects that are not in thermal equilibrium. Heat is not a property of an object.
One mole of an ideal gas in a sealed rigid container is initially at a temperature of 100 degrees C. The temperature is then increased to 200 degrees C. The pressure of the gas (a) remains constant (b) increases by about 25% (c) doubles (d) triples
answer: (b) increases by about 25% A common error is to treat the temperature as doubling. If the temperature doubled, the pressure would also double. However, the temperature is given in degrees Celsius, not kelvins. When the temperature is converted to kelvins, it is easy to see that the temperature only increases by about 25%, from 373 K to 437 K. The pressure then also increases by about 25%. (The actual amount is 26.8%.)
When an ideal gas is warmed from 20 degrees C to 40 degrees C, the gas's temperature T that appears in the ideal gas law increased by a factor (s) of 2 (b) of 1.07 (c) that depends on the temperature scale you use
answer: (b) of 1.07 The absolute (Kelvin) scale must be used in the ideal gas law. If the Celsius scale is used, it appears that the temperature has doubled. However, 0°C is an arbitrarily chosen point on the temperature scale and cannot be used to determine temperature ratios. When the temperatures are converted to kelvins (293 K and 313 K) it can be seen that their ratio is about 1.07.
A steel plate has a hole in it with a diameter of exactly 1.0 cm when the plate is at a temperature of 20 degrees C. A steel ring has an inner diameter of exactly 1.0 cm at 20 degrees C. Both the plate and the ring are heated to 100 degrees C. Which statement is true? (a) the hole in the plate gets smaller, and the opening in the ring gets larger. (b) The opening in the ring gets larger, but we need the relative size of the plate and the hole to know what happens to the hole. (c) the hole in the plate and the opening in the ring get larger. (d) The hole in the plate and the opening in the ring get smaller. (e) The hole in the plate and the opening in the ring gets smaller.
answer: (c) the hole in the plate and the opening in the ring get larger. Many students have the misconception that as the plate expands, the hole will get smaller. To understand what actually happens, imagine that the hole is filled with a steel disk. As the plate and the steel disk are heated, both will expand. After the plate and disk are heated, the disk is removed from the plate. Since the disk expanded, the hole that is left must also have expanded. As the steel ring is heated its circumference will expand, causing its interior to also expand.
An ideal gas is in a sealed rigid container. The average kinetic energy of the gas molecules depends most on (a) the size of the container (b) the number of molecules in the container (c) the temperature of the gas (d) the mass of the molecules
answer: (c) the temperature of the gas
Which of the following is not true about an ideal gas? (a) the average kinetic energy of the gas molecules increases as the temperature increases. (b) the volume of an ideal gas increases with temperature if the volume is held constant c) The pressure of an ideal gas increases with temperature if the volume is held constant (d) All gas molecules have the same speed at a particular temperature (e) The molecules are assumed to be far apart compared to their size
answer: (d) All gas molecules have the same speed at a particular temperature The temperature of an ideal gas is a measure of the average kinetic energy of the gas, so increasing the temperature will increase the average kinetic energy—(a) is true. Even though the temperature is proportional to the average kinetic energy of the molecules, each molecule canhave a random kinetic energy (according to the Maxwell distribution of speeds). The speeds of individual molecules will vary about this average, so (d ) is false. Per the ideal gas law, the product of the pressure and volume is proportional to the temperature. Therefore, if pressure or volume is held constant as the temperature increases, the other parameter (volume or pressure) must increase, so (b) and (c) are true. For a gas to be ideal, it is assumed that the space occupied by the gas is mostly empty. For this to be true, the molecules are assumed to be far apart compared with their size. Thus, (e) is also true.
Radiation is emitted (a) only by glowing objects such as the Sun (b) only by objects whose temperature is greater than the temperature of the surroundings (c) only by objects with more caloric than their surroundings (d) by any object not at 0 K (e) only by objects that have a large specific heat
answer: (d) by any object not at 0 K Radiation is emitted by all objects not at absolute zero. Very hot objects, such as the Sun, emit radiation in the visible spectrum, so they appear to be glowing. If the temperature of an object is less than that of its surroundings, it has a net gain in energy as it absorbs more radiation than it emits. However, it is still emitting radiation. The amount of radiation emitted is independent of the object's specific heat.
A typical thermos bottle as a thin vacuum space between the shiny inner flask (which holds a liquid) and the shine protective outer flask, often stainless steel. The vacuum space is excellent at preventing (a) conduction (b) convection (c) radiation (d) conduction and convection (e) conduction, convection, and radiation
answer: (d) conduction and convection Heat is able to transfer through a vacuum by radiation, but heat requires a medium to transfer by conduction and by convection. Therefore, the vacuum in a thermos prevents heat loss by conduction and convection.
The temperature of an ideal gas increases. Which of the following is true? (a) the pressure must decrease. (b) the pressure must increase. (c) The pressure must increase while the volume decreases. (d) the volume must increase while the pressure decreases (E) the pressure, the volume, or both may increase.
answer: (e) A common misconception is that if the temperature increases, both the pressure and volume will increase. However, by the ideal gas law, when the temperature increases, the product of the pressure and volume must increase. This increase can occur by increasing the pressure, increasing the volume, or both.
Two ideal gases, A and B, are at the same temperature. If the molecular mass of the molecules in gas A is twice that of the molecules in gas B, the molecules' root-mean-square speed is (a) the same in both gases (b) twice as great in A (c) 1.4 times greater in A (d) twice as great in B (e) 1.4 times greater in B
answer: (e) 1.4 times greater in B Some students might erroneously relate the temperature of the gas to the velocity of the gas molecules and surmise that the rms speeds would be equal. However, when the two gases are at the same temperature, the molecules will have the same average kinetic energy. The kinetic energy is proportional to the mass of the molecule and the square of the rms speed. Since mass B is half the mass of A, the speed of molecules of mass B must be 2 ≈ 1.4 × greater than the speed of molecules of mass A.
When you put an ice cube in a glass of warm tea, which of the following happens? (a) cold flows from the ice cube into the tea (b) cold flows from the ice cube into the tea and hear flows from the tea into the ice cube (c) Heat flows from the tea into the ice cube. (d) Neither heat nor cold flows . Only temperature flows between the ice and the tea..
answer:(c) Heat flows from the tea into the ice cube. A common misconception is that "cold" flows from the ice into the tea. When the ice is placed in the tea, the ice has less kinetic energy per molecule than the tea, so in molecular collisions between the tea and ice, energy transfers from the tea into the ice. This energy transfer cools the tea as it melts the ice and then heats up the ice. The transfer of energy from the warmer tea to the colder ice is called "heat."
Heat is (a) a fluid called caloric (b) a measure of the average kinetic energy of atoms (c) the amount of energy transferred between objects as a result of a difference in temperature (d) an invisible, odorless, weightless substance (e) the total kinetic energy of an ideal gas
answer:(c) the amount of energy transferred between objects as a result of a difference in temperature Students often think that heat is a substance or a property of a material. When two materials are at different temperatures (that is, they have different average kinetic energies per molecule), energy can transfer from the hot object to the cold object. This transfer of energy is called heat.