- #1

gabu

- 5

- 0

Please post this type of questions in HW section using the template.

The Clausius-Clapeyron formula is given by

[itex] \frac{d P}{d T} = \frac{L}{T \Delta V}[/itex]

where P and T are the pressure and temperature at the boiling point, respectively, and L is the latent heat per mole at the boiling point, and [itex]\Delta V[/itex] is the change in the volume per mole between the gas and liquid phases. For water, find the value of [itex](dP/dT)_{T=T_{0}}[/itex] when the pressure is 1 atmosphere and the temperature the boiling temperature [itex]T_{0}[/itex]. Consider the latent heat to be [itex]L = 540cal/g[/itex] and the gas constant as [itex]R=2.0\,cal\, mol^{-1}K^{-1}[/itex]

b) If the temperature of air and water inside the pressure cooker prior to heating is [itex]T_{1}(<T_{0})[/itex] , then how many atmospheres does the internal pressure of the cooker P reach when the temperature due to heating increases to T? Assume the water doesn't boil

Now... for the first part of the question I only have to determine the variation in volume at the boiling point so I can calculate the quantity asked. My idea to determine such variation is to use that

[itex]P\Delta V = R T[/itex]

but I'm not sure if I can use this equation for water vapour. Can it be considered an ideal gas? My idea is that, if it can, the volume per mole of vapour under those conditions is the variation in the volume of water.

For the second question, my idea is to integrate Clausius-Clapeyron equation but, I don't know the relation between [itex]\Delta V[/itex] and T or P. The only relation that comes to my mind is the ideal gases relations, but if I am to assume the water does not boil I can't use this relation. Which relation should I use?

Thank you very much.

[itex] \frac{d P}{d T} = \frac{L}{T \Delta V}[/itex]

where P and T are the pressure and temperature at the boiling point, respectively, and L is the latent heat per mole at the boiling point, and [itex]\Delta V[/itex] is the change in the volume per mole between the gas and liquid phases. For water, find the value of [itex](dP/dT)_{T=T_{0}}[/itex] when the pressure is 1 atmosphere and the temperature the boiling temperature [itex]T_{0}[/itex]. Consider the latent heat to be [itex]L = 540cal/g[/itex] and the gas constant as [itex]R=2.0\,cal\, mol^{-1}K^{-1}[/itex]

b) If the temperature of air and water inside the pressure cooker prior to heating is [itex]T_{1}(<T_{0})[/itex] , then how many atmospheres does the internal pressure of the cooker P reach when the temperature due to heating increases to T? Assume the water doesn't boil

Now... for the first part of the question I only have to determine the variation in volume at the boiling point so I can calculate the quantity asked. My idea to determine such variation is to use that

[itex]P\Delta V = R T[/itex]

but I'm not sure if I can use this equation for water vapour. Can it be considered an ideal gas? My idea is that, if it can, the volume per mole of vapour under those conditions is the variation in the volume of water.

For the second question, my idea is to integrate Clausius-Clapeyron equation but, I don't know the relation between [itex]\Delta V[/itex] and T or P. The only relation that comes to my mind is the ideal gases relations, but if I am to assume the water does not boil I can't use this relation. Which relation should I use?

Thank you very much.