First Law of thermodynamics (Theory questions) Flashcards
Consider these scenarios and state whether work is done by the system on the environment
(SE) or by the environment on the system (ES): (a) opening a carbonated beverage; (b) filling a
flat tire; (c) a sealed empty gas can expands on a hot day, bowing out the walls.
a. SE; b. ES; c. ES
When a liquid is vaporized, its change in internal energy is not equal to the heat added. Why?
Some of the energy goes into changing the phase of the liquid to gas.
Is it possible for the temperature of a system to remain constant when heat flows into or out of
it? If so, give examples.
Yes, as long as the work done equals the heat added there will be no change in internal energy
and thereby no change in temperature. When water freezes or when ice melts while removing or
adding heat, respectively, the temperature remains constant.
Does adding heat to a system always increase its internal energy?
If more work is done on the system than heat added, the internal energy of the system will
actually decrease.
When a gas expands isothermally, it does work. What is the source of energy needed to do this
work?
The system must be in contact with a heat source that allows heat to flow into the system.
Most materials expand when heated. One notable exception is water between 0 °C and 4 °C,
which actually decreases in volume with the increase in temperature. Which is greater for water
in this temperature region, CP or CV?
Typically CP is greater than CV because when expansion occurs under constant pressure, it does
work on the surroundings. Therefore, heat can go into internal energy and work. Under constant
volume, all heat goes into internal energy. In this example, water contracts upon heating, so if we
add heat at constant pressure, work is done on the water by surroundings and therefore, CP is less
than CV.
It is unlikely that a process can be isothermal unless it is a very slow process. Explain why. Is
the same true for isobaric and isochoric processes? Explain your answer.
Isothermal processes must be slow to make sure that as heat is transferred, the temperature does
not change. Even for isobaric and isochoric processes, the system must be in thermal equilibrium
with slow changes of thermodynamic variables
Is it possible for γ to be smaller than unity?
No, it is always greater than 1.
There is no change in the internal energy of an ideal gas undergoing an isothermal process
since the internal energy depends only on the temperature. Is it therefore correct to say that an
isothermal process is the same as an adiabatic process for an ideal gas? Explain your answer.
An adiabatic process has a change in temperature but no heat flow. The isothermal process has
no change in temperature but has heat flow.
A gas follows pV = bp + c on an isothermal curve, where p is the pressure, V is the volume,
b is a constant, and c is a function of temperature. If c can be determined from the measurement
of a single other thermodynamic parameter, it establishes a temperature scale for this gas. Show
that a temperature scale under an isochoric process can be established with this gas, with
pressure being the measured parameter, and is identical to that of an ideal gas.
p(V - b) = −c is the temperature scale desired and mirrors the ideal gas if under constant
volume.
In a quasi-static isobaric expansion, 500 J of work are done by the gas. If the gas pressure is
0.80 atm, what is the fractional increase in the volume of the gas, assuming it was originally at
20.0 L?
1.4 times
It takes 500 J of work to compress quasi-statically 0.50 mol of an ideal gas to one-fifth its
original volume. Calculate the temperature of the gas, assuming it remains constant during the
compression.
74 K
An ideal gas expands quasi-statically and isothermally from a state with pressure p and
volume V to a state with volume 4V. Show that the work done by the gas in the expansion is pV(ln 4).
pVln(4)
What is the internal energy of 6.00 mol of an ideal monatomic gas at 200 C° ?
3.53 x 10^4 J
Two monatomic ideal gases A and B are at the same temperature. If 1.0 g of gas A has the
same internal energy as 0.10 g of gas B, what are (a) the ratio of the number of moles of each gas
and (b) the ration of the atomic masses of the two gases?
a. 1:1; b. 10:1
In an expansion of a gas, 500 J of work are done by the gas. If the internal energy of the gas
increased by 80 J in the expansion, how much heat does the gas absorb?
580 J
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Two moles of helium gas are placed in a cylindrical container with a piston. The gas is at
room temperature 25 C° and under a pressure of 5 3.0 10 Pa. × When the pressure from the outside
is decreased while keeping the temperature the same as the room temperature, the volume of the
gas doubles. (a) Find the work the external agent does on the gas in the process. (b) Find the heat
exchanged by the gas and indicate whether the gas takes in or gives up heat. Assume ideal gas
behavior.
a. −3 400 J; b. 3400 J enters the gas
The temperature of an ideal monatomic gas rises by 8.0 K. What is the change in the internal
energy of 1 mol of the gas at constant volume?
100 J
If the gases of the preceding problem are initially at 300 K, what are their internal energies
after they absorb the heat?
a. 370 J; b. 100 J; c. 500 J
A monatomic ideal gas undergoes a quasi-static adiabatic expansion in which its volume is
doubled. How is the pressure of the gas changed?
pressure decreased by 0.31 times the original pressure
When 400 J of heat are slowly added to 10 mol of an ideal monatomic gas, its temperature
rises by 10 °C. What is the work done on the gas?
0.31
A dilute gas expands quasi-statically to three times its initial volume. Is the final gas pressure
greater for an isothermal or an adiabatic expansion? Does your answer depend on whether the
gas is monatomic, diatomic, or polyatomic?
Isothermal has a greater final pressure and does not depend on the type of gas.
An ideal diatomic gas at 80 K is slowly compressed adiabatically and reversibly to half its
volume. What is its final temperature?
106 K
Compare the charge in internal energy of an ideal gas for a quasi-static adiabatic expansion
with that for a quasi-static isothermal expansion. What happens to the temperature of an ideal gas
in an adiabatic expansion?
An adiabatic expansion has less work done and no heat flow, thereby a lower internal energy
comparing to an isothermal expansion which has both heat flow and work done. Temperature
decreases during adiabatic expansion.
A hand-driven tire pump has a piston with a 2.50-cm diameter and a maximum stroke of 30.0
cm. (a) How much work do you do in one stroke if the average gauge pressure is 5 2 2.4 10 N/m ×
(about 35 psi)? (b) What average force do you exert on the piston, neglecting friction and
gravitational force?
a. 59.5 J; b. 170 N
A helium-filled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How
much greater is the internal energy of the helium in the balloon than it would be at zero gauge
pressure?
300 J
Four moles of a monatomic ideal gas in a cylinder at is expanded at constant pressure
equal to 1 atm until its volume doubles. (a) What is the change in internal energy? (b) How much
work was done by the gas in the process? (c) How much heat was transferred to the gas?
a. 15,000 J; b. 10,000 J; c. 25,000 J
