Question

An iron rod of length 50m and at a temperature of 80°C is heated to 90°C. Calculate its new length. The linear expansivity of iron is 1.2×10^-5 K^-1.

a) 50.0006 m
b) 50.0012 m
c) 50.0001 m
d) 50.0003 m

Answer 1

To calculate the new length of the iron rod after heating, we apply the linear thermal expansion formula. The change in length due to the 10°C increase is 0.006 m, resulting in a new length of 50.006 m, which is closest to option a) 50.0006 m.

Step-by-step explanation:

The subject at hand involves the concept of linear thermal expansion in Physics. The student is trying to calculate the change in length of an iron rod when its temperature is increased. To find the new length of the iron rod after heating, we use the formula ΔL = αLΔT, where ΔL is the change in length, α is the linear expansivity (also known as the coefficient of linear expansion), L is the original length of the material, and ΔT is the change in temperature.

Plugging in the given values:

• α (linear expansivity of iron) = 1.2×10-5 K-1
• Original length (L) = 50 m
• Temperature increase (ΔT) = (90 - 80)°C = 10°C

Calculating the change in length ΔL:

ΔL = 1.2×10-5 × 50 × 10 = 0.006 m

The new length of the iron rod after being heated to 90°C is:

Lnew = Original length (L) + Change in length (ΔL)

Lnew = 50 m + 0.006 m = 50.006 m

Out of the options provided by the student, the closest to our calculated new length is 50.0006 m which corresponds to option a).