question_answer 6)

A steel tape 1 m long is correctly calibrated for a temperature of \[{{27.0}^{o}}C\] . The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is \[{{45.0}^{o}}C\]. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is \[{{27.0}^{o}}C\]? Coefficient of linear expansion of steel \[=1.20\times {{10}^{-5}}{{\,}^{o}}{{C}^{-1}}\].

Answer:

Length of the steel tape at \[{{27}^{o}}C\] is 100 cm. i.e. L = 100 cm and \[T={{27}^{o}}C\] . The length of steel tape at \[=37\times {{10}^{9}}\text{N }{{\text{m}}^{\text{2}}}\]is \[atm=1\cdot 013\times {{10}^{5}}pa.\]= \[\text{p=10 atm}=10\times 1\cdot 013\times {{10}^{5}}\]Length of 1 cm mark at \[{{27}^{o}}C\] on this scale, at \[pa;B=37\times {{10}^{\text{9}}}\text{N }{{\text{m}}^{\text{-2}}}\]cm. Length of 63 cm measured by this tape at \[{{45}^{o}}C\] will be \[=\frac{100.0216}{100}\times 63=63.0136\,cm\].