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Q.

The air tight and smooth piston of a cylindrical vessel are connected with a string, as shown. Initially pressure and temperature of the gas are P₀ and T₀ . The atmospheric pressure is also P0 . At a later time, tension in the string is $\frac{3}{8} P_{0} A$ where A is the cross sectional area of the cylinder. At this time, the temperature of the gas has become.

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a

$\frac{11}{8} T_{0}$

b

$\frac{3}{8} T_{0}$

c

$\frac{3}{4} T_{0}$

d

$\frac{13}{8} T_{0}$

answer is C.

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Detailed Solution

$T = P_{0} A = P A T = (P - P_{0}) A$ $= \frac{3}{8} P_{0} A (given) P = \frac{3}{8} P_{0} + P \frac{11}{8} P_{0}$

Now volume is constant by string So, $P α T$

Initial temperature is T₀

$Now as pressure has become \frac{11}{8} P_{0},$ $temperature will be \frac{11}{8} T_{0}$ .

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The air tight and smooth piston of a cylindrical vessel are connected with a string, as shown. Initially pressure and temperature of the gas are P0 and T0 . The atmospheric pressure is also P0 . At a later time, tension in the string is 38P0A where A is the cross sectional area of the cylinder. At this time, the temperature of the gas has become.