$2 \times 10^{10} \textrm{ W}$

### Solution video

# OpenStax College Physics, Chapter 14, Problem 51 (Problems & Exercises)

### Calculator Screenshots

*M*by multiplying both sides by

*V*, so mass is volume multiplied by density. So, we substitute for that in place of

*M*. We write that here in red. And then, substitute all of this in place of

*Q*in our power formula. So, power is going to be volume times density times specific heat times change in temperature divided by time. And, I'm rewriting this slightly by writing this as volume over time times rho

*C*

*Delta T*because volume over time is something that we're given directly. It is this quantity, five times ten to the five cubic meters per day. So, we have five times ten to the five cubic meters per day, but we have to write day in units of seconds in order to have

*M*

*K*

*S*units as we need to have in almost all of our formulas. So, one day times 24 hours per day times 3600 seconds per hour gives us a day in seconds. And so, all this gets multiplied by 2700 kilograms per cubic meter density times 840 Joules per kilogram per Celsius degrees specific heat of granite, times 30 degrees Celsius minus 1200 degrees Celsius. And so, we have a power output of -1.536 times ten to the ten watts. And so, this is power being lost, and so we'll write it as a positive number here by saying it's power lost by the lava, two times ten to the ten watts. And, we can have only one significant figure here because we have this volume rate of transfer is only one significant figure.

## Comments

For some reason I got this problem wrong because the T1 and T2 were switched. So I got it correct with the answer 1.53x10^10.

Are you referring to the temperatures at 2:23? $30^\circ\textrm{C} - 1200^\circ\textrm{C}$? That's written as final temperature minus initial temperature, or $T_2 - T_1$ in other words. Let me know your thoughts.

Yes, I'm saying the answer that my homework program accepted was a result of switching the temperature to (T1-T2 ) instead of (T2-T1).

Hello, thank you for the follow up. It sounds like your homework system was expecting a positive answer? The formula gives "heat transfer to the lava", whereas your homework system is asking for "the heat transfer **from** the lava". The question asks for "heat transfer out of Earth" which I take to mean the heat transfer **from** the lava, which is why I expressed the final answer as a positive as well.