Question

P2D.1' According to the Intergovernmental Panel on Climate Change (IPCC) the global average temperature may rise by as much as 2.0 °C by 2100. Predict the average rise in sea level due to thermal expansion of sea water based on temperature rises of 1.0 °C, 2.0°C, and 3.5 °C, given that the volume of the Earth's oceans is 1.37 x 10°km3 and their surface area is 361 x 10 kmt; state the approximations which go into your estimates. Hint: Recall that the volume V of a sphere of radius r is V = 4nr'. If the radius changes only slightly by 8r, with 8r <<r, then the change in the volume is SV 4nr'8r. Because the surface area of a sphere is A = 4tr?, it follows that 8V- Aôr.

Answer 1

Amswev: Givm, (volume ol Cavthtsoleom) e 1.37x l09 km3 Suvlate Ava 361x lo6 km2 Thvough thivmal expousiom d Sa water vavics with Jattovs tompevature, prissuve, Savimity like we have Asumd the thevmal Coelecint of A V Vxoc pomsion (or) = 9x104 /00 xis Coulled the ractiomal Volunse Chongt pev Rui tmperatuve unit Rises by o'c 9tomp = 9x lo4/0 (ea uatom) A v 13 x 1x1 = x lox 1.39 x l7 kms.74 x lo5 km AV

i Radius, Sh <<h. Jor Small Chong wi ton AssimmL Sv AV(4x h2) x Sh -ltguatiom-1) hongeu Rodius Sealevel) SuyJate Ava Volume) the Value tqua hom- By puttig 2.24 x los km3- 361 x l0 km2x Sh 4 x 10S km3 2 61 x l06 km =2.59 x lo Km (se i Sea level lov chc) S o759 m

Rises 2 °C tempera tuve by 1 . euatom using 2 x lo4/0c A v レメ20L Av x l04x 1-37 x lo km3 x 2 5-48 x105 Km3 AV= Astwing Av (4ns2) x Sh Sh <くh 548 ×10s km3 = 361 メlob kml x Sカ. 5.48 x lo5km3 S 3.61 x 106km 2 1.51x 1o km 1.51m hisc Stalevel lov 2 ° ise T

Similarly lov 35% hise AV Vx3.50C AV=2x 164 x 137 x lo km3 x 3.5 - 9.59 x 105 km 8カくくろ →Av= (4nh1)メ Sh 9.59 x105 km3 3.6l x lob kmx Sh 9.65 x 102 km Sh .65 m Rise lor per 3.5 Rise m temperatuve