Question

2. You mix 50 grams of ice at 0.0 degrees C and 50 grams of steam at 100 degrees celsius. What is the equilibrium temperature? The earth receives on average 240 W of power per square meter. Using the Stefan-Boltzmann law, calculate the predicted average Earth’s temperature (assume e=1). From a web-search find the average Earth temperature and the primary reason the value you calculated is too low?

Answer 1

Part 1) On mixing the ice and steam, Assume that there is no loss of heat, So that

Heat lost by 50g steam should be equal to heat received by 50g ice ...........

Latent heat to ice at 0°c to convert into saturated water at 0°c + sensible heating of this saturated water from 0°c to final temp T°c = cooling of hot water from 100°c to final temp T°c

=> where Latent heat of fusion =

= Specific heat capacity of water =1 cal/g/°c

Putting value we get

Part 2) The Stefan-Boltzmann Law says that the emitted radiation is equal to a constant times the effective radiating temperature raised to the fourth power.

Radiation emitted by the Earth = constant x T⁴ where contant is 5.67 x 10^-8 W /m²/K^4,

Temperature is in Kelvin(K)

Radiation emitted by the Earth = Radiation received by the Earth =

This effective temperature of 255 K is the temperature the Earth's Surface would have, if it didn't have an atmosphere. It would be awfully cold! In reality, the Earth's surface temperature is closer to 288 K (15 °C, 59 °F). This difference of 33 K is the magnitude of the greenhouse effect.