If length of major arc is 88 and radius is 7 then find area of major segment
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Question
The temperature of an ideal gas at an initial pressure P1 and volume V1 is increased at constant volume until the pressure is doubled.
The temperature of an ideal gas at an initial pressure P1 and volume V1 is increased at constant volume until the pressure is doubled. The gas is then expanded isothermally until the pressure drops to is original value, where it is compressed at constant pressure until the volume returns to its initial value. (a) sketch these process in the P-V plane and in the P-T.
To find the area of the major segment, we first need to find the angle of the major arc.
The formula to find the length of a major arc is given by:
Length of major arc = (θ/360) × 2πr
Where θ is the angle of the major arc and r is the radius.
Rearranging the formula, we can find the angle of the major arc:
θ = (Length of major arc / (2πr)) × 360
θ = (88 / (2π * 7)) × 360
θ ≈ 238.73 degrees
Now that we have the angle of the major arc, we can find the area of the major segment.
The formula to find the area of a segment is given by:
Area of segment = (θ/360) × πr^2 - (r^2/2) × sin(θ)
Where θ is the angle of the segment and r is the radius.
Plugging in the values:
Area of segment = (238.73 / 360) × π * 7^2 - (7^2/2) × sin(238.73)
Area of segment ≈ 69.07 square units
Therefore, the area of the major segment is approximately 69.07 square units.