Q. A brass wire of length 2 m and radius 1 mm at 27°C is held taut between two
rigid supports. Initially it was cooled to a temperature of −43°C creating
a tension T in the wire. The temperature to which the wire has to be cooled
in order to increase the tension in it to 1.4T, is ____ °C.
Explanation
For a wire held between rigid supports, thermal stress is directly proportional
to the change in temperature.
Initial temperature drop:
\[
\Delta T_1 = 27 - ( -43 ) = 70^\circ\text{C}
\]
This temperature change produces tension T in the wire.
To increase the tension to \(1.4T\), the temperature change must be:
\[
\Delta T_2 = 1.4 \times \Delta T_1 = 1.4 \times 70 = 98^\circ\text{C}
\]
Let the final temperature be \( \theta \).
\[
27 - \theta = 98
\]
\[
\theta = 27 - 98 = -71^\circ\text{C}
\]
Therefore, the required temperature is −71°C.