Final answer:
The altitude at which the temperature would be -50°C is approximately 10.8 km above Earth's surface, and the depth at which the temperature would be 1500°C within Earth's interior is roughly 59.2 km.
Step-by-step explanation:
Using the information given, we can predict the altitude at which the temperature would be -50°C in the atmosphere and the depth at which the temperature would be 1500°C within Earth's interior. For the atmosphere, we know that the temperature decreases by about 6.5 K per km. Starting from a base temperature of 293 K (20°C), if we want to reach -50°C (which is 223 K), we'd need to account for a change in temperature of 70 K. Dividing this temperature change by the lapse rate (6.5 K/km), we find that this temperature would be encountered at an altitude of approximately 10.8 km above Earth's surface.
For Earth's interior, temperature gradients can vary, but let's assume a typical geothermal gradient of about 25°C per km in the Earth's crust. To reach a temperature of 1500°C, starting from a surface temperature of 20°C, a change of 1480°C is needed. Dividing 1480°C by 25°C/km, we predict that the depth would be roughly 59.2 km.