Two cylinders fitted with pistons and placed as shown, connected with string through a small tube of negligible volume, are filled with a gas at pressure P_o and temperature T_o. The radius of smaller cylinder is half of the other. If the temperature is increased tp 2T_o, find the pressure, if the piston of bigger cylinder moves towards left by 1 meter ?

\(\frac{5}{4}P_o\)

Initial volume = 1 x [\(\pi R^2 + \frac{\pi R^2}{4}\)] = \(\frac{5}{4}\pi R62\)

Piston moves towards left by 1 m on heating. Additional volume available due to heating is :

  = 1 x \(\pi R^2\) - \(\frac{1*\pi R^2}{4}\) = \(\frac{3}{4} \pi R^2\)

Total volume after heating = 2 \(\pi R^2\)

\(P_o*\frac{5}{4}\pi R^2 = nRT_o\)

After heating : \(P_2 * 2\pi R^2 = nR * 2T_o\)

\(\frac{P_1}{P_2} \frac{5}{4} \frac{1}{2} = \frac{1}{2}\)

\(P_2 = \frac{5P_o}{4}\)