5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. d. What amount of heat energy is transferred from the gas as its pressure decreases?

Video transcript

Hi, everyone in this breakfast problem, we're being asked to determine how much heat energy is transferred from uh 4 g of oxygen gas that initially has a volume of 2.5 liters and a pressure of four A PM. The gas is then compressed at a constant pressure until the volume is reduced by health and finally undergoes an iso choric process until the gas reaches its original temperature of 25 degrees Celsius. The options given are a 477 Joles B 774 jules, C 387 Joles and the jos. So in this particular practice problem, we will consider the gas as ideal. So I'm just gonna write that down here to indicate our assumption that we made ideal guess. So the number of moles of gas or N will be equal to M divided by a mole, which in this case, I'm just gonna indicate that with a mole, which in this case can be calculated by taking the mass of 4.00 g divided by the molecular weight, which is going to be 32 g per mole for oxygen because in this case, we're talking about oxygen. So then the number of moles can be calculated to be equal to 0.125 mole, which is the total moles of oxygen. In this container, the gas will undergo an isobaric compression. Therefore, the ideal gas relationship can be reduced to P two divided by T two equals to P one divided by T one during the isobaric compression or decompression with equal pressure. But in this case, feed two is given to be half of P one or P one divided by two and T one is given to be 25 degrees Celsius, which in this case, we want to convert that into Kelvin, which will then be equal to 2 25 plus 273. Kelvin, which will be equals to 298. Kelvin. The um temperature T two can then be obtained by actually rearranging our isobaric um equation or expression which will then come out to be T two to then be equal to P two multiplied by T one divided by P one. So let's substitute the values that we have. So in this case, we want to substitute P two with P one divided by two. So T two will then come out to be equal to P one divided by two, multiplied by T one divided by uh P one. So in this case, we can cross out the P ones and T two will then just be T one divided by two, which will come out to be 298 Kelvin divided by two, which will come out to be 149 Kelvin. So now that we have obtained P two, we can look at the next process which is, which is an ISO process so that the volume is constant and the temperature returns to its original value. So the heat exchange during this uh iso process will actually be then transferred to the gas. Therefore, the heat energy transferred from the gas will have, we can uh can be calculated using this formula where Q will be equals to N multiplied by CV multiplied by delta T. So let's substitute the values that we have. And we have calculated the uh number of moles previously to be 0. moles. So let's substitute that 0.125 moles multiply that with the CV, which will be a constant for oxygen, which is 20.8 joles divided by mole. Kelvin multiply that with delta T which will be the difference between 298 Kelvin and 149 Kelvin. So 290 Kelvin minus 1 49 Kelvin and then calculating this, we will get the Q to then be equal to 387 jus. So the total amount of heat energy transferred from the gas will be equal to 387 Jules, which actually will correspond to option C in our answer choices. So option C will be the answer to this particular practice problem and that will be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topic available on our website. But other than that, that'll be it for this video. And thank you.