Question

Consider an isothermal cylinder and massless piston assembly in which ideal gas is filled. Cross-sectional area of the cylinder = 1 m². Three masses m₁, m₂ and m₃ are kept on the piston. When m₁ is removed, the piston moves upto point A. When m₁ and m₂ both are removed piston moves upto point B and when m₁, m₂ and m₃ all three are removed, piston moves upto point C. The work done by the gas is ______ J, when piston moves from point B to point C.

[Given : m₁ = 2 × 10⁴ kg, m₂ = 3 × 10⁴ kg, g = 10 m/s²]

विकल्प

• 1000

• 1053

• 1500

• 3200

Answer 1

Consider an isothermal cylinder and massless piston assembly in which ideal gas is filled. Cross-sectional area of the cylinder = 1 m². Three masses m₁, m₂ and m₃ are kept on the piston. When m₁ is removed, the piston moves upto point A. When m₁ and m₂ both are removed piston moves upto point B and when m₁, m₂ and m₃ all three are removed, piston moves upto point C. The work done by the gas is 3200 J, when piston moves from point B to point C.

Explanation:

Initially piston is at equation,

`10^6 = ((2 xx 10^4 + 3 xx 1064 + "m"_3)xx10)/1 + 10^5`

`"m"^3 = ((10^6 - 10^5)/10) - 5 xx 10^4`

= 10⁴ (10 - 1) - 5 × 10⁴

= 10⁴ (9 - 5) = 4 × 10⁴ kg

since T = constant

P_iV_i = P_BV_B

`10^6 xx 4 = (10^5 + 4 xx 10^5) xx "V"_"B"`

`"V"_"B" = (4 xx 10^6)/(10^5 xx 5) = 40/5` = 8 lit.

Also, 

P_BV_B = P_CV_C 

10⁴ × 5 × 8 = 10₅ × V_C

V_C = 40 L

W_BC = - P_ext (V_C - V_B)

= - 10⁵ (40 - 8) × 10^-3

= - 3200 J

W_by = 3200 J