Question

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 non-trivial numerical answer is 2%. To avoid rounding errors, use the unrounded intermediate values in your final calculations. Let's assume the initial volume of the gas is 2.00 L, the initial temperature of the gas is 30.0 °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 = 9.52×10^(-2) mol You now heat the gas slowly until the temperature reaches 55.2 °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? It moves up When the final temperature is reached, you stop heating the gas. Part C What is the final pressure of the gas? P = 1.20 bar Part D What is the final volume of the gas? V = 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 55.2 °C. It moves up It stays in the same position It moves down Part F What is the sign of w? positive zero negative Part G What is the value of w? Be careful with units. How do you convert bar*L to J? w =

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 non-trivial numerical answer is 2%. To avoid rounding errors, use the unrounded intermediate values in your final calculations.

Let's assume the initial volume of the gas is 2.00 L, the initial temperature of the gas is 30.0 °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 = 9.52×10^(-2) mol

You now heat the gas slowly until the temperature reaches 55.2 °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?
It moves up

When the final temperature is reached, you stop heating the gas.

Part C
What is the final pressure of the gas?
P = 1.20 bar

Part D
What is the final volume of the gas?
V =

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 55.2 °C.
It moves up
It stays in the same position
It moves down

Part F
What is the sign of w?
positive
zero
negative

Part G
What is the value of w? Be careful with units. How do you convert bar*L to J?
w =

Added by Charles R.