A gas in a cylinder expands from a volume of 0.110 m^3 to 0.320 m...

Question

A gas in a cylinder expands from a volume of 0.110 m^3 to 0.320 m^3 . Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 * 10^5 Pa during the expansion. The total heat added is 1.15 * 10^5 J. (a) Find the work done by the gas.

Accepted Answer

Hey everyone in this problem. We have a lab experiment with a student using a piston cylinder assembly. Okay. Initially containing 10 cm cubed of an ideal gas. The cylinders heated with an electric resistor to maintain constant pressure of the gas. The net energy added to the gas by heat is five jewels and the pressure sensor inside the cylinder indicates a value of three times 10 to the five pascal's and were asked to find the work done by the gas. If the volume of the cylinder is doubled. Alright, now let's think we're told that we have a constant pressure. Okay, this means that we are in ice a bear conditions. Okay. And when we have ice bear conditions, we know that we can write the work W O K is equal to p the pressure times a change in volume. V two minus V one. Okay. All right. So we're looking for the work. W and we have this equation because of the ice a bear conditions. Let's think about what we have. Okay, p is the pressure? We're given the pressure here and the problem. Okay, three times 10 to the five pascal's and then we want to find the change in volume. What we're given the initial volume. Okay, so we have p the pressure is three times 10 to the five pascal's. Okay, we have the initial volume V I or sorry, V one is equal to 10 centimeters. Cute. Hey, converting this into our standard units. This is gonna be one times 10 to the negative 5m cubed an RV to our final V were not given an direct value but we're told that it's going to be doubled. Okay so this is just going to be equal to two times V one which is going to be two times 10 to the negative five m stooped. Okay, so now we have P. V. One and V. Two. We have everything we need to find the work. W So the work W. Is equal to P three times 10 to the five pascal's times the change in volume, two times 10 to the negative five m cubed minus one times 10 to the negative five m cubed. Well this is gonna equal on the right hand side. We're just gonna get one times 10 to the negative five. Okay. When we multiply 10 to the five times 10 to the negative five we add the exponents to get zero. Okay, so we're gonna have 10 to the zero. So times one and we end up with just three jewels. And so the work done here, it's going to be three jewels. That's gonna correspond with answer A. That's it for this one. I hope this video helped see you in the next one

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