This problem continues Exercise 1. However, note that the initial volume and temperature may have changed due to variable randomization. Pay attention to the values stated below and use them in all your calculations for this excercise.
In exercise 1 the piston was allowed to move freely. Now, you put stoppers on the piston so it cannot move up or down.
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.
The initial volume of gas is 4.20 L , the initial temperature of the gas is 32.0 °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).
Then, as you did in Exercise 1, you heat the gas slowly until the temperature reaches 57.2 °C
Part A
How many moles of gas are there in the container?
n =
mol
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Part B
What is the final volume after you reach the final temperature?
V =
L
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Part C
What is the final pressure after you reach the final temperature?
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?
w =
J
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2 Frictionless piston, can move up or down
Challenge: pV work 1
Consider a container with a frictionless piston that contains a given amount of an ideal gas.
Letâs assume that initially the external pressure is 2.20 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is 0.500 L and the initial temperature is 25°C.
Now, you will increase the volume of the gas by changing the external pressure slowly in a way that guarantees that the temperature of the system remains constant throughout the process. To do this, imagine you remove the pebbles one by one slowly to increase the volume by an infinitesimal amount. Every time you remove a weight you allow the system to equilibrate. Your cylinder is immersed in a water bath at 25°C, which keeps your gas at the same temperature throughout the whole process.
Remember to use three significant figures for all numerical answers. The margin of error for each numerical answer is 1%. To avoid rounding errors use the unrounded intermediate values in your final calculations.
Note: You may find an equation to solve this problem in a textbook or online, but the goal of this challenge is that you think through the problem and come up with the equation on your own. This problem requires basic calculus, so be ready to integrate!
Part A
What is the volume of the gas when you remove all pebbles?
V =
L
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Part B
What is the final pressure of the gas?
p =
bar
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Part C
Now consider the work performed by the sytem. What is the sign of w?
Now consider the work performed by the sytem. What is the sign of w?
