Saving a Town from Lava Thermodynamics Problem

[BrainMan]

Homework Statement

Homework Equations

Q₁ + Q₂ = 0

The Attempt at a Solution

I found the mass of water needed to cool the lava to a solid. I'm not sure how to find the rate of water needed to stop the lava.

https://lh3.googleusercontent.com/HTrvgt1wh2amrK8pZkIgNXe3HUaQ8lUPQHugcY-7NzMPqAZ1jAiB8ws4V4G_E60yfYe03KX23qTVAmIDJuXK7UYo3d685xqE5b0VxHk81jFFbijZbFhwrAP5OcGJV3EDHVH3F72QSP9x1rnut92wI3J-wRRGdXAG43ONxSehJns78s8QTpbIDqU0PT2dLxdQmvd4S6fxPRe4bqtLQG3g34A3aULY6daVs_c7wIFw0N7yQ3pQy1vt9ib6c0CN-rN54HAE8Vdv_yPFA0VMhPx219qiJkE1U5feFCZLKLH16J_ZW4ELwQ5q7eeJnFaZ1mJJsFFv2lmeZU94-WWUiUqUolKMTe1su0a6ejG-ElQLnHBAmzP7-O9briknyffQYrUoeW3T9OANjI21Sa2E73_PUByRrFxrdsHns4L0MARbTys-nXTVReSk1W_RTiFNvWK6mbPk5ChLxZ0uvjq-spgOINTkjj5y615fPGDQ0DKBnWwwssw8mSuso_BGrItJFAWEYhLwmIqIEy42yInjUPnUreOMqJ3hZjDSqhY2Dp654zeCbyUmKr4biZN7g9FFZv0SVxNLgowMuID6t1A1QiqgCwbfk0Rlf7639-l8D3DrAb5AK6UqaYII=w497-h662-no

 

[TomHart]

What happens to the water when it reaches 100 deg C?

I found the mass of water needed to cool the lava to a solid. I'm not sure how to find the rate of water needed to stop the lava.

The mass of lava you calculated (350000 kg) was the mass of lava that arrives every minute. So the mass of water needed every minute would have to cool that lava down from 1200 to 800 deg C and then freeze it. So it looks like that is what your mass of water is attempting to represent. But like I mentioned at the beginning, water doesn't increase in temp. from 20 to 800 deg C.

Edit: By the way, it looks like your 1.4 e11 and 1.54 e11 numbers are correct.

 

[BrainMan]

What happens to the water when it reaches 100 deg C?

The mass of lava you calculated (350000 kg) was the mass of lava that arrives every minute. So the mass of water needed every minute would have to cool that lava down from 1200 to 800 deg C and then freeze it. So it looks like that is what your mass of water is attempting to represent. But like I mentioned at the beginning, water doesn't increase in temp. from 20 to 800 deg C.

Edit: By the way, it looks like your 1.4 e11 and 1.54 e11 numbers are correct.

OK I see. So I need to add M_wL_v because the water is going to evaporate. Then I need to add nCΔT for water in the gas state until it reaches 800 deg C, right? But what should I use for C for water in the gas phase?

 

[TomHart]

That's the part I was wondering about. I was thinking that once the water turns to steam, it doesn't hang around to be heated up by the lava; it just rises upward never to be heard from again. At least that's what I think would happen.

 

[BrainMan]

That's the part I was wondering about. I was thinking that once the water turns to steam, it doesn't hang around to be heated up by the lava; it just rises upward never to be heard from again. At least that's what I think would happen.

OK you're right. You get the right answer if you just add MwLv. So basically, the Lava is heating up the water to boiling point and then the rest of the energy is removed when the water evaporates to a gas. The steam then "just rises upward never to be heard from again." Thanks!