A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20^ C , the calibration temperature for the scale. What would the scale read for the length of the rod when both are at 40^ C ? Given: for steel =11 10⁻⁶ per ^ C and for Cu =17 10⁻⁶ per ^ C

Step-by-step solution

Using the relation l_t=l₀(1+ t) aligned & =1 [1+11 10⁻⁶ (40^ -20^ ) ] & =1.00022 ~cm aligned Now length of copper rod at 40^ C aligned R_t ^ & =l₀ ^ (1+ ^ t ) & =80 [1+17 10⁻⁶ (40^ -20^ ) ] & =80.0272 ~cm aligned Now number of cms observed on the scale = 80.0272 1.00022 =80.0096