Let W_1 be the work done in blowing a soap bu | vedclass

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(D) The work done in blowing a soap bubble of radius $r$ is given by $W = T 	imes \Delta A$,where $T$ is the surface tension and $\Delta A$ is the ch

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$W_2 < 4 W_1$

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(D) The work done in blowing a soap bubble of radius $r$ is given by $W = T 	imes \Delta A$,where $T$ is the surface tension and $\Delta A$ is the change in surface area. Since a soap bubble has two surfaces,$\Delta A = 2 	imes (4 \pi r^2) = 8 \pi r^2$.Thus,$W_1 = 8 \pi r^2 T$,where $T$ is the surface tension at room temperature.For the second bubble of radius $2r$ formed from the heated solution,the work done is $W_2 = 8 \pi (2r)^2 T'$,where $T'$ is the surface tension at the higher temperature.$W_2 = 8 \pi (4r^2) T' = 32 \pi r^2 T'$.Since the soap solution is heated,its surface tension decreases,meaning $T' Comparing $W_1$ and $W_2$: $W_2 = 4 W_1 	imes (T'/T)$.Since $T' < T$,it follows that $W_2 < 4 W_1$.

Let $W_1$ be the work done in blowing a soap bubble of radius $r$ from a soap solution at room temperature. The soap solution is now heated and a second soap bubble of radius $2r$ is blown from the heated soap solution. If $W_2$ is the work done in forming this bubble,then:

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