Question #c13ab

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Answer 1 · 2016-10-29T17:25:13

#sf(1.96color(white)(x)"cm")#

Because the pressure remains constant we can use:

#sf(V_1/T_1=V_2/T_2)#

The volume of a sphere is given by:

#sf(V=4/3pir^3)#

So the expression becomes:

#sf((cancel(4/3pi)r_1^3)/T_1)#=#sf((cancel(4/3pi)r_2^3)/T_2)#

#:.##sf(r_2^3=r_1^3/T_1xxT_2)#

We need to convert to absolute temperature so:

#sf(T_1=8.50+273=281.5color(white)(x)"K")#

#sf(T_2=93.7+273=366.7color(white)(x)"K")#

Putting in the numbers:

#sf(r_2^3=(1.80)^3xx366.7/281.5)#

#sf(r_2^3=7.579)#

#:.##sf(r=""^3sqrt(7.579)=1.96color(white)(x)"cm")#

This seems a reasonable answer as you would expect the radius to increase as the temperature is raised.