Chp 13: Thermal Flashcards
What is meant by the absolute scale?
The scale is independent of any thermometric property of any substance
What is the concept of absolute zero in the thermodynamic temperature scale?
At absolute zero, all substances are said to have the smallest possible internal energy
Assumptions of ideal gas/kinetic theory of gases.
- The volume of particles is negligible compared to the volume of the gas.
- There are no intermolecular forces between the particles.
- The collision between all gas molecules and the walls is elastic and no energy is lost.
- The container contains a very large number of molecules in continuous random motion.
- The duration of collision is negligible compared to the duration between collisions.
- The particles obey Newton’s Laws of motion.
How molecular movement of gas particles causes gas pressure on the walls of a vessel?
A gas consists of a large number of molecules in continuous random motion in the vessel. When a molecule hits the wall, it experiences change in momentum due to the force exerted by the wall on the gas molecule, according to Newton’s 2nd law. By Newton’s 3rd law, the molecule exerts an equal but opposite force on the wall. The average total force per unit area exerted by all the molecules on the wall is the pressure on the wall
Explain why mean velocity of gas is zero?
The gas contains a large number of particles moving in random motion and in all directions. There is equal probability of finding 2 particles with the same speed but in the opposite direction, since velocity is a vector, the velocities add up to zero.
State what is meant by the thermal equilibrium of 2 bodies by reference to:
Temperature:
Movement of thermal energy:
Both bodies have the same temperature.
There is no net transfer of thermal energy between the 2 bodies.
Why temperature of a body is not the measure of the quantity of thermal energy stored in the body.
Temperature is the measure of the average kinetic energy of the molecules whereas thermal energy in a body is its internal energy. The thermal energy of the body, which is the internal energy includes both the microscopic kinetic energy and potential energy of the gas molecules.
Compare the pattern of the movement and speed of the molecules in water and water vapour at the same temperature.
Water molecules move in a continuous random motion within the liquid body whereas water vapour molecules move about freely in continuous motion within the container. Water molecules are more closely spaced and have restricted motion while water vapour molecules are further apart and move about freely over larger distances. However, since both are at the same temperature and temperature is a measure of the average kinetic energy of the molecules, both water and water vapour molecules have the same average microscopic kinetic energy and thus the same root mean square speed
Why when a gas within a container is brought into an airplane at a certain altitude and travelling at a certain speed has internal energy the same as if it were stationary on the ground floor?
The internal energy of a gas is the sum of random distributions of the total microscopic kinetic energy and potential energy of the gas molecules. The kinetic energy due to the random motion of gas molecules does not change even when it is in a moving airplane. The potential energy due to the intermolecular forces of attraction also does not change even if the container has larger gravitational potential energy. Thus, the internal energy does not change.
Under what conditions does a real gas behave like an ideal gas?
At low pressure and high temperature. When the gas is at low pressure, the molecules are very far apart, and hence they experience negligible intermolecular forces of attraction. When at high temperature, the molecules are moving at very high speed since the average KE of the gas molecules is directly proportional to the thermodynamic temperature of the gas. The intermolecular forces of attraction are negligible as potential energy is negligible
Explain, in terms of the force produced by the molecules of the gas, how the pressure remains constant as the volume increases and temperature increases.
The increase in temperature increases r.m.s. speed since the average microscopic kinetic energy is directly proportional to the thermodynamic temperature of the gas, and thus the change in momentum of each molecule colliding with wall of container. The increase in volume reduces frequency of collision of molecules with the walls of the container. Since force by each molecule is the rate of change of momentum of the molecule (by N2L), which is now increased, and the frequency of collision has decreased, the total force exerted by all the molecules on the walls of the container can remain constant (by N3L) Since pressure = force/area, the pressure can remain constant.
For a fixed mass of ideal gas, explain using kinetic theory of gases, what happens to its pressure when its volume is reduced at constant temperature?
Since the average microscopic kinetic energy of the gas molecules is directly proportional to the thermodynamic temperature of the gas, since the temperature is constant, the average kinetic energy and hence rms speed is constant. As volume decreases, the molecules will collide with the walls more frequently hence the change in momentum of the molecules occurs more frequently. By N2L, the total force exerted by the wall on molecules increases. By N3L, the total force by molecules on wall increases. Since pressure is the total force per unit area, the pressure of the gas increases.
What is the internal energy of an ideal gas?
It is the sum of random distribution of the microscopic kinetic energy of all the gas molecules as the potential energy is zero due to negligible intermolecular forces for an ideal gas.
By reference to the energy of molecules, explain why the internal energy of an ideal gas is proportional to its thermodynamic temperature.
The internal energy of a real gas is the sum of random distribution of the microscopic kinetic energies and potential energies of all gas particles. However, for an ideal gas, since intermolecular forces of attraction are negligible, the potential energy is zero, as such, the internal energy of an ideal gas is solely the sum of random distribution of the kinetic energies of the gas particles. Since the total microscopic kinetic energy of an ideal gas is 3/2NKT, where N is the number of particles, K is the Boltzmann’s constant and T is the thermodynamic temperature, the internal energy of an ideal gas is proportional to its thermodynamic temperature
Using the 1st law of thermodynamics, why is the constant pressure specific heat capacity larger than the constant volume specific heat capacity.
By the first law of thermodynamics, the increase in internal energy, ∆U, is the sum of thermal energy supplied to, Q and the work done on the system, Won. (∆U = Q + Won). Hence, Q = ∆U - Won = ∆U + Wby. At constant pressure, the gas will expand, doing positive work by the gas. Hence, the thermal energy supplied to the gas will not only increase the internal energy and therefore the temperature, but also do positive work to expand. However, for the constant volume case, there is no change in volume hence no work done by gas. The thermal energy supplied is only used to increase the internal energy. Since the increase in internal energy is the same for both cases, the constant pressure specific heat capacity is larger than constant volume
