Two gases A and B are filled at the same pres | vedclass

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(B) According to the first law of thermodynamics,$Q = \Delta U + W$.Since the heat supplied $Q$ is the same and the change in internal energy $\Delta

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$\frac{3}{4}$

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(B) According to the first law of thermodynamics,$Q = \Delta U + W$.Since the heat supplied $Q$ is the same and the change in internal energy $\Delta U$ is the same for both gases,the work done $W$ must also be the same.$W_A = W_B$Since the pressure $P$ is constant,the work done is $W = P \Delta V = P (A \Delta x)$,where $A$ is the area of the piston and $\Delta x$ is the displacement.$P (\pi r_A^2) \Delta x_A = P (\pi r_B^2) \Delta x_B$Given $\Delta x_A = 16 \ cm$ and $\Delta x_B = 9 \ cm$.$r_A^2 (16) = r_B^2 (9)$$\frac{r_A^2}{r_B^2} = \frac{9}{16}$Taking the square root on both sides,we get $\frac{r_A}{r_B} = \sqrt{\frac{9}{16}} = \frac{3}{4}$.

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