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.