Consider a vertical tube open at both ends. The tube consists of two parts, each of different cross-sections and each part having a piston which can move smoothly in respective tubes. The two pistons are joined together by an inextensible wire. The combined mass of the two pistons is 5 kg and area of cross-section of the upper piston is $10 c m^{2}$ greater than that of the lower piston. Amount of gas enclosed by the pistons is one mole. When the gas is heated slowly, piston moves by 50cm. Find rise in the temperature of the gas, in the form $\frac{70 + 2 X}{R}$ Kelvin, where R is universal gas constant. Use $g = 10 m / s^{2}$ and outside pressure $= 10^{5} N / m^{2} .$ Find the value of X.

Question

Consider a vertical tube open at both ends. The tube consists of two parts, each of different cross-sections and each part having a piston which can move smoothly in respective tubes. The two pistons are joined together by an inextensible wire. The combined mass of the two pistons is 5 kg and area of cross-section of the upper piston is $10 c m^{2}$ greater than that of the lower piston. Amount of gas enclosed by the pistons is one mole. When the gas is heated slowly, piston moves by 50cm. Find rise in the temperature of the gas, in the form $\frac{70 + 2 X}{R}$ Kelvin, where R is universal gas constant. Use $g = 10 m / s^{2}$ and outside pressure $= 10^{5} N / m^{2} .$ Find the value of X.

Accepted Answer

Due to heating pressure inside is changed. Let inside pressure  P then for equilibrium of the system.P(A1−A2)=Po(A1−A2)+(m1+m2)g PΔV=(PoΔA+mg)l  ΔT=(PoΔA+mg)lnR  ΔT=75R  but given  ⇒70+2xR⇒2x=5⇒x=2.5

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