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Consider a vertical tube open at both en...

Consider a vertical tube open at both ends. The tube consists of two parts, each fo different cross-section and each part having a piston which can move smoothly in respective tubes. The two pistons are joined togther by an inextensible wire. The combined mass of the two piston is `5kg` and area of cross-section of the upper piston is `10cm^(2)` greater than that of the lower piston. Amount of gas enclosed by the pistons is one mole. When the gas is heated slowly, pistons move by `50cm` as shown in figure. The rise in the temperature of the gas, in the form `(X)/(R)K` where `R` is universal gas constant. Use `g = 10 m//s^(2)` and outside pressure `= 10^(5) N//m^(2))`. Fill value of `X`.

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The correct Answer is:
3
Due to the heating pressure inside in not changed. Let inside pressure be `rho`. Then for equilibrium of the system.

`P(A_(1)-A_(2))=P_(0)(A_(1)-A_(2))+(m_(1)+m_(2))g`
`impliesP/_\V=(P_(0)/_\A+mg)L`
`L` is displacement of the piston.
`P./_\V=nR/_\T`
`/_\T=(P/_\V)/(nR)=((P_(0)/_\V+mg)L)/(nR)`
`=((10^(5)P_(a)xx10^(-3)m^(2)+5xx10)(50xx10^(-2)))/(1xxR)=75/R K`
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