A monatomic ideal gas that is initially at 1.50 * 10^5 Pa and has...

Question

A monatomic ideal gas that is initially at 1.50 * 10^5 Pa and has a volume of 0.0800 m^3 is compressed adiabatically to a volume of 0.0400 m^3. (a) What is the final pressure?

Accepted Answer

Hey everyone welcome back in this problem. We have a sample of helium. Okay. With an initial volume of 0.14 m cubed and an initial pressure of 2.45 times 10 to the five pascal's okay. It's compressed idiomatic lee to a final volume of 0.7 m cubed. And were asked to calculate the final pressure. We're told to treat helium like an ideal gas. Okay. And that it's mono mono atomic. All right, so we have idea batic li we think no heat transfer. Okay, let's write out what we know. We know the initial volume. V one is 0.14 m cute. Okay, we know the initial pressure P one is 2.45 Times 10 to the five Pascal's. We know that V two is equal to 0.07 m cubed. Okay. The final volume and we want to find P to the final pressure. Okay, so this is an idea biotic process. So let's think about the relationship between Pressure and volume. In an idea biotic process recall that we can write P one. V 1 to the exponent. γ Is equal to P two. V 2 to the exponent camera. Alright, so we have P one. We have the sorry we have P one. We have V one. We have V two. We want to find P two and what we're missing is gamma. Okay. Alright, so let's work on the side here. We have gamma and this is the ratio of heat capacities. Okay. And let's recall it's going to be the ratio heat capacity pressure and volume. Maybe we don't know either of these yet. What do we know though? We know that helium is mono atomic because helium is mono atomic. Okay. This tells us that CV is going to equal to 3/2 times. Are the gas constant? Okay. Okay. So we have C V. We still need to find gamma which means we need C. P. Or some information about Cp. Okay. We're also told that we can treat this gas as ideal. We have an ideal gas. We have a relationship between Cp and CV given by C P is equal to Cv plus are okay but we know Cv. So this is just going to be three half our Plus our which is going to be 5/2 our. Alright so now we have cp we have cv we can find gamma or ratio of heat capacities. This is five halves are Divided by 3/ are Which is equal to 5/3. Can I? Alright so we have our gamma. The exponent that we need to use in our pressure volume equation here let's go ahead and substitute the rest of the values. So we have P 12.45 times 10 to the five pascal's. Okay we have V one which is 0.14 m cubed to the exponent five thirds And this is going to equal to P two which we don't know we're looking for. Okay. Times V 20.7 m cubed to the exponent five thirds. When we work this out we're gonna find P. Two. Okay we're gonna multiply here and then divide by the 0.7 to the exponent five thirds. The units of meters cube to the exponent. 5/3 will cancel. We're gonna be left with P. Two equal to 7.78 times 10 to the five pascal's. Okay. And so that is the final pressure we were looking for. That's going to correspond with answer D. That's it for this one. I hope that video helped see you in the next video.

A monatomic ideal gas that is initially at 1.50 * 10^5 Pa and has a volume of 0.0800 m^3 is compressed adiabatically to a volume of 0.0400 m^3. (a) What is the final pressure?

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