The lower yield point for an iron that has an average grain diameter of 1 × 10–2 mm is 230 mpa. at a grain diameter of 6 × 10–3 mm, the yield point increases to 275 mpa. at what grain diameter will the lower yield point be 310 mpa? express the answer in mm to three significant figures

Explanation:

We need to find the constant for the particular material given by the yield strenght equation,

That is,

Where

The yield strenght

Average grain diameter

constant for the particular material

Our values are,

Substituting for mm and 230Mpa for ,

(1)

Substituting for and 275Mpa for ,

(2)

Solving the two values (1) and (2) we have,

Substituting now for 310Mpa calculate 310Mpa

Solving for d,

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas