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Aparcel of air with a volume of 6.8 * 104 kmn} rises to an altitude where all the water in the parcel condenses and increases the temperature of the air; parcel by ...

Question

Aparcel of air with a volume of 6.8 * 104 kmn} rises to an altitude where all the water in the parcel condenses and increases the temperature of the air; parcel by 4.8PC. What is the mass of water in the air parcel? (Assume the density of air at tle condensation altitude 7.6 * 102 Pin ! The latent heat of vaporization Of water is 540 caVg. and the specific heat of air is 0.17 caVg"C ) Express the answer in standard scientific notation;

Aparcel of air with a volume of 6.8 * 104 kmn} rises to an altitude where all the water in the parcel condenses and increases the temperature of the air; parcel by 4.8PC. What is the mass of water in the air parcel? (Assume the density of air at tle condensation altitude 7.6 * 102 Pin ! The latent heat of vaporization Of water is 540 caVg. and the specific heat of air is 0.17 caVg"C ) Express the answer in standard scientific notation;



Answers

When steam condenses to liquid water, $2.26 \mathrm{~kJ}$ of heat is released per gram. The heat from $168 \mathrm{~g}$ of steam is used to heat a room containing $6.44 \times 10^{4} \mathrm{~g}$ of air $(20 \mathrm{ft} \times$ $12 \mathrm{ft} \times 8 \mathrm{ft}$ ). The specific heat of air at normal pressure is $1.015 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)$. What is the change in air temperature, assuming the heat from the steam is all absorbed by air?

So here we're going to use the ideal gas law. The pressure terms of volume equals the number of most times the ideal gas, constant times a temperature. Now we can say that the number of moles divided by the volume would be equaling the pressure divided by the ideal gas. Constant times t the temperature. Ah, we're going to then solve and say that this is gonna be equaling 7.34 times 10 to the third Newtons per square meter, divided by 8.31 Jules Perk, Calvin Permal multiplied by the temperature of 313.15 Calvin. And so we have that the moles per unit volume would be equaling 2.82 moles per cubic meter. And so we know that the density is equaling the number of moles per cubic per unit volume or per cubic meter times Mm ah, the Moler mass of water. And so the density would be equaling 2.82 moles. Ah, per unit volume in this case, cubic meters multiplied by the molar mass of water, 18.0 grams Permal. And this is equal in approximately 50.8 grams per cubic meter. Um and this is approximately equal to what is given 51.1 grams per cubic meter. This would be the saturation vapor density, but this would be our final answer. So it is about 0.3 grams per cubic meter off. That is the end of the solution. Thank you for one.

Question Number 43 wants you to prepare a figure similar to a figure found on page three or 5 38 figure ah 15. 15. It shows positive. Delta H is a formation from elements to form no to and negative. Delta H is of formation when forming eso three from the elements. So we will start from the elements that form water in the gas phase and in the liquid phase. The elements that are used to form water are molecular, hydrogen and molecular oxygen, Molecular hydrogen and molecular oxygen both have delta h of formation values of zero, so they will be up here high in our figure. Then the delta H of formation of gaseous H 20 is negative 241 8 killed jewels, Permal and the formation of hydrogen. Our water liquid is negative to 85.8 kg goals per mole. So this means mawr energy is released in the formation of liquid water than in gaseous water. To determine the delta h of vaporization. It's simply going to be the difference in Delta H is of formation of liquid water and gaseous water, meaning we want to go from liquid water to gaseous water to solve for the Delta h of this process. Delta, referring to change, is always final state at this Delta H value, minus the initial state at this Delta H value. So we'll take the final state at negative 241.8 killed jewels for mole minus the initial state at negative to 85.8 kg per mole. And we get positive. 44 kill a Jules per mole and it should be positive because we need to add energy in to go from the liquid state to the gaseous state, meaning we need to go up the energy diagram as shown here.

So the first calculation we have to look at today in this podcast related to physical chemistry is the relative humidity. So just for context, relative humidity equals y a p over p A. T multiplied by 100. So what we have is P 35 degrees C. That is equal to 42.175 millimeters mercury. He the 20. We see these both for water. Each to, um is 17.535 millimeters of mercury. And so what we take is why h 20 That's the in light of the A is equal to R H multiplied by Pete Star H 20 35 degrees seat by the by p. So we consult for this equation and getting a point, not 491 miles of h 20 per mole of that. Now we can calculate the mole fraction of water in the outlet Airstream a 20 degrees C. We'll do it on the next page. We have Y H 20 is equal to P star H 20 20 divided by pressure and as he do not point not 2 to 7 miles of H 20 per mile of. So next we have the following equation to consider. I'll start a fresh page for this parts we have n So, uh, at the outlet is equal to P v doctor at the outlet of our TR At the outlet, we plug in our values. For this we got 5 to 8.1 MPH. So the most of the into the A C unit will equal the malls out of the A C unit of birth. So with some substitution, we get to the following equation that in is equal to one take away, not point not for 91 moles of H 20 the morals of a so that is equal to 5 to 8 0.1 MPH. One take we're not point not 2 to 7 polls H 20 bye bye malls. What we get is 542.8 MPH between calculate the volumetric flow right now that is V equal to N. R. T over P. What we get is a body off 13 1005 5 liters per hour. So I actually can take a look at the amount of moisture that is condensed. So what we have is, um h 20 is equal to m capitalism, each 12 multiplied by gamma h two. This is all in and to track gamma age to out out what's what by end up. So what? We get this value of not 0.264 kg per hour.

You know, the same three assumptions were going today, so I'm not specifying here. You may have understood all the three assumptions should now. So I just proceed with the question here. So here also, we have the pressure as 18 p. M. And considering the properties off the air at various states, it can be determined from the psychometric char or the es. Hence we get the values off the air to be Each one is it's too. Then we have it. Three This is that the human defecation sector. All these values were getting using the psychometric child or the es. Then we have specific humidity to do this on the specific humidity at the human defecation part is different. Does this So these give these up obtained from the E s child? No analyzing all these properties and the values that we have, we understand that the specific humanity at the inlet is equal to the specific humanity at the outlet or the exit. This is in case of the heating section at the unification sector. We have this specific humidity to be greater than that of the exit level. Now the amount of C magic can be is Delta. So that is the difference between the specific humidities. So considering that we have the amount of heat added to be right, so this is what is our amount of heat Add now, the heat transfer of the air is what we have to find out at the heating section on that can be found out by the equation. The difference in the entire piece of the inlet on the exit part. So this is the heat transfer off the air, the heating section per unit.


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