When a 200g block is placed on the piston, the volume of the gas goes from 5×10−5m3 to 4.7×10−5m3, while the pressure goes from 5.4×104Pa to 5.7×104Pa . If the surface area of the piston is 1×10−3m2 , the energy transferred to the gas due to the compression is most nearly

The energy transferred to the gas is 9 mJ

Explanation:

Given;

initial volume of the gas, v₁ = 5 x 10⁻⁵ m³

final volume of the gas, v₂ = 4.7 x 10⁻⁵ m³

initial pressure of the gas, P₁ = 5.4 x 10⁴ Pa

final pressure of the gas, P₂ = 5.7 x 10⁴ Pa

The work done in compressing the gas is given by;

W = ΔPV = (P₂ - P₁)(V₂ - V₁)

W = (5.7 x 10⁴ Pa - 5.4 x 10⁴ Pa)(4.7 x 10⁻⁵ m³ - 5 x 10⁻⁵ m³)

W = (3000)( -3 x 10⁻⁶)

W = - 9  x 10⁻³ J

W = -9 mJ

Thus, the work done in compressing this gas is equal to the energy transferred to the gas = 9 mJ

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