Exam 2 Conceptual Questions
When doubling temperature what scale do you use?
Absolute Temperature Scale (Kelvins)
A sample of water vapor in an enclosed cylinder has an initial pressure of 500 Pa at an initial temperate of -0.01°C. A piston squeezes the sample smaller and smaller, without limit. Describe what happens to the water as the squeezing progresses.
As the piston squeezes the sample the pressure increases. As the pressure on the gas increases from that initial point on the phase diagram it passes from the gas region to the solid region and eventually to the liquid region.
Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2. Would the molar specific heat at constant volume change? If so, by what factor? If not, why not?
Cv would not change because it only depends on the kind of gas, not on the temperature or speed of the molecules
What is the highest temperature at which ice can exist?
Ice does not exist for temperatures greater than the triple point of water
How do you convert from Fahrenheit to Celsius?
T(°C) = (T(°F) - 32) × 5/9 (Subtract 32 and Multiply by 5/9)
Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2. Would the temperature of the gas increase by factor of 2^(1/2), 2, or 2^(2)?
The temperature will increase by a factor of 2^(2) because v^(2)rms = ((3kT)/m)
A gas is in a sealed container. By what factor does the gas pressure change if the volume is halved and the temperature is tripled?
p2=(V1/.5V1)(3T1/T1)p1=6p1
A gas is in a sealed container. By what factor does the gas pressure change if the volume is doubled and the temperature is tripled?
p2=(V1/2V1)(3T1/T1)p1=3/2p1
A gas is in a sealed container. The gas pressure is tripled and the temperature is doubled. By what factor does the number density of the gas increase?
(n1/V1)=(p1/RT1)(n2/V2)=(p2/RT2)=(3p1/R(2T1))(n2/V2) =(3/2)(n1/V1)
A piston is sitting still. How do we know that the pressure is equal?
If the pressure was unequal the piston would accelerate to equilibrium
Does (a)temperature, (b)heat, and (c)thermal energy describe a property of a system, an interaction of the system with its environment, or both?
(a)Temperature is a property of a system related to the thermal energy per molecule (b)Heat is the energy transferred between the system and the environment. Heat may cause the thermal energy to change, but that doesn't mean that heat and thermal energy are the same. (c)Thermal energy is a state variable and property of the system. It continues to exist even if the system is isolated and not interacting with the environment
What is absolute zero?
0K -459.67°F
A sample in an experiment is initially at 10°C. If the sample's temperature is doubled, what is the new temperature in °C?
10°C = 283K 2(283K) = 566K = 293°C
By what factor does the gas temperature change if the volume is halved and the pressure is tripled?
3/2T1 T2=((3p1/p1)(.5V1/V1))T1
By what factor does the gas temperature change if the volume is doubled and the pressure is tripled?
6T1 T2=((3p1/p1)(2V1/V1))T1
An aquanaut lives in an underwater apartment 100m beneath the surface of the ocean. Compare the freezing and boiling points of water in the aquanaut's apartment to their values at the surface. Are they higher, lower, or the same?
Freezing Point - Lower Boiling Point - Higher Solid-liquid transition line in the phase diagram has a negative slope, but the liquid-gas transition line has a positive slope. Since there is more air pressure at 100m it will take less to freeze the water but more to boil it since it requires a larger temperature under larger pressures
Two containers hold equal masses of nitrogen gas at equal temperatures. You supply 10 J of heat to container A while not allowing its volume to change, and you supply 10 J of heat to container B wile not allowing its pressure to change. Afterward is temperature T_A greater than, less than, or equal to T_B?
Greater Than. Q=nCvΔT(A)=nCpΔT(B)=10 J n_A=n_B CvΔT(A)=CpΔT(B) Cp>Cv ΔT(A)>ΔT(B)
The mean free path of molecules in a gas is 200nm. What will be the mean free path if the pressure is doubled while the temperature is held constant?
If pressure is doubled, the mean free path is halved to 100nm. λ ∝ (1/(N/V) and (N/V) = (p/(kT)) so at constant temperature λ ∝ 1 /p
The mean free path of molecules in a gas is 200nm. What will be the mean free path if the absolute temperature is doubled while the pressure is held constant?
If temperature is doubled, the mean-free path is doubled to 400nm. (N/V) = (p/(kT)) so at constant pressure λ ∝ T
Why is the molar specific heat of a gas at constant pressure larger than the molar specific heat at constant volume?
In a constant-volume process all heat input is used to increase the temperature of the gas. But in a constant-pressure process, since some work is done, some energy leaves the system as work. So more heat is needed to produce the same ΔT Cp>Cv
Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2. Would the rms speed of the molecules increase by a factor of 2^(1/2), 2, or 2^(2)?
It would increase by a factor of 2. The average increase is a factor of 2; the square root of 2 squared is 2.
Suppose you place an ice cube in a beaker of room-temperature water, then seal them in a rigid, well-insulated container. No energy can enter or leave the container. Finding a large ice cube and some 100 C steam would not violate the first law of thermodynamics. W = 0J and Q = 0J because the container is sealed, and ΔEth = 0J because the increase in thermal energy of the water molecules that became steam is offset by the decreased in thermal energy of the water molecules that tuned to ice. Energy would be conserved, yet we never see an outcome like this. Why not?
It would violate the second law of thermodynamics.
If the pressure of a gas is really due to the rand collisions of molecules with the walls of the container, why do pressure gauges -even sensitive ones- give perfectly steady readings? Shouldn't they continually be fluctuating?
No, because there are such an unbelievably large number of collisions every second, and the force of each is unbelievably small, that even a sensitive gauge can't show a response to each and every collision.
Is there a lowest temperature at which water vapor can exist?
No, the positive slope of the solid-vapor boundary begins at the point (0 K,0 atm). This means that as long as pressure is low enough, water can always exist in the vapor phase.
When a space capsule returns to earth its surfaces get very hot as it passes through the atmosphere at high speed. Has the space capsule been heated?
No. There is not a transfer of energy due to a temperature difference. When the shuttle re-enters the atmosphere there is friction between the molecules of the atmosphere and the shuttle. The mechanical energy of the shuttle is transformed into thermal energy. The initial kinetic energy of the shuttle decreases.
A gas is in a sealed container. The gas pressure is tripled and the temperature is doubled. Does the number of moles of gas in the container increase, decrease, or stay the same?
Stays the same The gas is in a sealed container so no moles are gained or lost
Rank from highest to lowest temperature - T1 = 0K, T2 = 0°C, and T3 = 0°F
T2>T3>T1
The density of air at STP is about (1/1000) the density of water. How doe sthe average distance between air molecules compare to the average distance between water molecules?
The distance between molecules in air is about 10 times the distance between molecules in water. If all the linear dimensions of a substance are increased by a factor of 10, making the distances between molecules 10 times larger, the volume of the substance increases by a factor of (10^3)=1000 and its density (inversely proportional to volume) decreases by a factor of 1000.
Gases, in contrast with solids and liquids, are very compressible. What can you infer from the observation about the microscopic nature of gases?
The fact that a gas is easily compressed tells us that the atoms/molecules are very far apart in comparison with the actual size of an atom or molecule. There's lost of empty space that can be squeezed.
Solids and liquids resist being compressed. They are not totally incompressible, but it takes large force to compress them even slightly. If it is true that matter consists of atoms, what can you infer about the microscopic nature of solids and liquids from their incompressiblility?
The fact that liquids and solids can't be compressed tells us that the atoms/molecules of liquids and solids are essentially in contact with each other and can't be squeezed any closer together.
Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2. Would the gas pressure increase by factor of 2^(1/2), 2, or 2^(2)?
The pressure would increase by a factor of 2^(2) = 4 because p ∝ v^(2)rms
You need to raise the temperature of a gas by 10°C. To use the lease amount of heat energy, should you heat the gas at constant pressure or at constant volume?
To use the least amount of heat energy you should heat the gas at constant volume. nCvΔT<nCpΔT Cv<Cp
Suppose you place an ice cube in a beaker of room-temperature water, then seal them in a rigid, well-insulated container. No energy can enter or leave the container. If you open the container an hour later, will you find a beaker of water slightly cooler than room temperature, or a large ice cube and some 100 C steam?
You expect to find a cup of water slightly cooler than room temperature. heat energy will not transfer spontaneously from a cooler system to a warmer system, but they had a long enough time to reach equilibrium.