Boiling Water at High Pressure. When water is boiled at a pressur...

Question

Boiling Water at High Pressure. When water is boiled at a pressure of 2.00 atm, the heat of vaporization is 2.20 * 10^6 J/kg and the boiling point is 120°C. At this pressure, 1.00 kg of water has a volume of 1.00 * 10^-3 m^3 , and 1.00 kg of steam has a volume of 0.824 m^3. (a) Compute the work done when 1.00 kg of steam is formed at this temperature.

Accepted Answer

Hey everyone in this problem. We have a chef who wants to reduce the cooking time by a few minutes. Okay. So to do this, he raises the pressure to four atmospheres inside the cooker. Okay. And then he's gonna stay at this pressure? We're told the boiling point of water the density of water and the density of steam. Okay, 100 and 44 degrees Celsius, 922.2 kg per meters cubed and 2. kg per meter cube respectively. And were asked what is the work done By 200 g of steam. Okay. All right, so let's think about this. We're inside the cooker. We're at a constant pressure. Ok, So you raised the pressure to a particular value and then left it there. So we have a constant pressure which means we're in ice bear conditions. Okay, We're looking for the work. What do we know about the work in icy conditions? Well, let's recall that we can write. The work is equal to p the pressure times V two minus V. One. Okay. The change in volumes. Alright, well, we know the pressure P. Okay, we're giving this four atmospheres is equal to four times 1.13 to times 10 to the five pascal's, which is equal to 4.53 times 10 to the five pascal. Okay, this is our standard unit that we want to be in when we're writing pressure in this equation, or absolute pressure. Alright, so we have p the pressure. What about the volumes we aren't given volumes but what we are given is masses and densities. Alright, so what's go ahead and find Our volumes. Okay, let's start with water. Okay, and this is going to be our first volume. Okay, we're starting with water and we're producing steam. So water is going to be our V1. Okay. And let's recall the relationship between density, mass and volume. So we have the density is equal to the mass divided by the volume. We are looking for the volume. We know the density. Okay, so V one is going to be mass divided by density. The mass we're given is 200 g. So we have 0.2 kg. Okay, divided by the density and the density of water. It's going to be 922.2 kg per meter cube. And this is going to give a V1 of 2.168 7, 3 times 10 to the -4 m. Cute. Okay. Alright, so we have this the first volume again, we have our pressure over here. Now we just need to find V one in order or sorry, V two in order to calculate the work w that we're looking for. Okay, so let's deal with steam now. Okay, we're going to call this volume two because this is the final volume. Yet the density is equal to the mass divided by the volume just like in the case of water. Okay, so the volume is gonna be the mass which is still 0.2 kg Divided by the density. And the density were given is 2. kilogram per meter cubed, which gives a volume V 20. meters. Alright, so now we have our density, we have both of our volumes. We can go ahead and calculate our work in our isobars conditions. So let's do that. So the work is equal to p times of change in volume V two minus V one which is equal to 4.053 times 10 to the five Pascal's times 0. m cubed minus 2.16873 times 10 to the negative four m cubed. This is going to give us a work of 3. times 10 to the four jewels. Okay, and so that is the work done. And going back up to our problem, work done by this steam. It's gonna be C 3.73 times 10 to the four jewels. Thanks everyone for watching. I hope this video helped see you in the next one

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