Question

pV work - Exercise 1

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 P_int > P_ext and vice versa. The piston will stop moving when P_int = P_ext (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 don’t 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.

Let’s 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. Let’s 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