Work is determined by the external pressure expansion of a gas into a vacuum does no work. Expansion of the gas dv is positive. If internal is greater than external, gas will expand. Expansion will continue and pint will decrease until pint = pext. While pint>pext it is irreversible and spontaneous. The piston will not reverse direction and compress the gas. At equilibrium the system is reversible because it could just as easily go one way as the other. Maximum work is obtained when pext is as large as it can be. Expansion will not occur if pext > pint. Thermal energy is a form of kinetic energy in which the center of the mass of the system does not change. When thermal energy flows from one system from another is is called heat. Heat and work are path dependent their sum is independent of path. This function is the internal of a system.
Consider a container with a frictionless piston that contains a given amount of an ideal gas. If the external pressure is kept constant, the piston will move up or down in response to a change in the internal pressure. The piston will move up if Pint > Pext and vice versa. The piston will stop moving when Pint = Pext (the system is equilibrated).
The following problem will slowly guide you through a work calculation. Some questions may appear trivial, so trust your instincts and donât assume there are hidden tricks. The goal of such a guided exercise is to help you picture the situation so you understand how all relevant variables change or stay the same. This is the first in a sequence of related problems.
Remember to use three significant figures for all numerical answers. The margin of error for each numerical answer is 5%. To avoid rounding errors use the unrounded intermediate values in your final calculations.
Letâs assume the initial volume of the gas is 3.90 L , the initial temperature of the gas is 26.0 °C , and the system is in equilibrium with an external pressure of 1.2 bar (given by the sum of a 1 bar atmospheric pressure and a 0.2 bar pressure due to a brick that rests on top of the piston).
Part A
How many moles of gas are there in the container?
n =
mol
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You now heat the gas slowly until the temperature reaches 51.2 °C You do it slowly so the piston can move if necessary until a new equilibrium is reached.
Part B
What happens with the piston while you heat the gas?
What happens with the piston while you heat the gas?
It moves up
It stays in the same position
It moves down
When the final temperature is reached, you stop heating the gas.
Part C
What is the final pressure of the gas?
P =
bar
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Part D
What is the final volume of the gas?
V =
L
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Part E
What happens with the piston after you finish heating the gas? Assume you do not need to worry about the gas cooling down again because the outside of the container is at a lower temperature. That is, you manage to keep the gas at a constant temperature that equals 51.2 °C
What happens with the piston after you finish heating the gas? Assume you do not need to worry about the gas cooling down again because the outside of the container is at a lower temperature. That is, you manage to keep the gas at a constant temperature that equals 51.2
It moves down
It moves up
It stays in the same position
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So far this was all at the level of your general chemistry class. Letâs now calculate the work involved in the process. Recall the sign conventions we use in physical chemistry, and always think from the point of view of the system (the gas).
Part F
What is the sign of w?
What is the sign of w?
negative
positive
zero
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Part G
What is the value of w? Be careful with units. How do you convert bar*L to J?
