Question

What is its diameter when the temperature is raised to 100 degrees Celsius? (b) What temperature change is required to increase its volume

Answer 1

The question is incomplete, the complete question is;

A spherical steel ball bearing has a diameter of 2.540cm at 25.00∘C.

(a) What is its diameter when it's temperature is raised to

100∘C?

(b) What temperature change is required to increase its volume by

1.000% ?

Answer:

a) 2.542 cm

b) 303.03°C

Explanation:

Given;

Diameter of the ball= 2.540cm

Initial temperature= 25.0°C

Final temperature= 100.0°C

Percentage increase in volume = 1.000%

Temperature coefficient of expansion for steel =11.0×10^−6/∘C

d2= d1[1 + α(T2-T1)]

d2= 2.540[1 + 11.0×10^−6(100-25)]

d2= 2.540[1 + 8.25×10^-4]

d2= 2.542 cm

From;

%V ×1/100 = V ×3α ×∆T/ V

Substituting values;

1.000 ×1/100= 3× 11.0×10^−6 × ∆T

∆T= 0.01/3× 11.0×10^−6

∆T= 303.03°C