Question

The temperature gradient in a rod of 0.5m long is $80^{\circ}$ C/m. If the temperature of hotter end of the rod is $30^{\circ}$ C, then the temperature of the cooler end is____

Answer 1

Hint: A temperature gradient is a quantitative parameter that indicates the direction and rate at which temperature varies around a specific area. The temperature gradient is a physical quantity that is measured in degrees (on a certain temperature scale) per unit length. Kelvin per metre (K/m) is the SI unit

Complete answer:
Temperature gradient is directly proportional to the temperature difference between two places and inversely proportional to the length or distance between the two sites. This indicates that as the length or distance between two places increases, the value of the temperature gradient reduces, and as the temperature differential between two sites increases, the temperature gradient likewise increases.
Given in the question, Length of the rod, $l=0.5m$
The temperature gradient in the rod= $80{}^\circ c/m$
Temperature of the hotter end of the rod, ${{\theta }_{1}}=30{}^\circ c$

Formula of the temperature gradient is
Temperature gradient= $\dfrac{{{\theta }_{1}}-{{\theta }_{2}}}{l}$
Where ${{\theta }_{2}}$ is the temperature of the colder part

Now putting the given value in the formula of the temperature gradient mentioned above,
$Tg=\dfrac{{{\theta }_{1}}-{{\theta }_{2}}}{l}$
$80=\dfrac{30-{{\theta }_{2}}}{0.5}$
$40=30-{{\theta }_{2}}$
${{\theta }_{2}}=-10{}^\circ c$

Therefore, the temperature on the cooler side of the rod is -10 degree Celsius.

Note: In the atmospheric sciences, temperature gradients in the atmosphere are crucial. It is extremely useful in climatology, meteorology, and weathering. It also has a variety of additional applications. The dynamics of the atmosphere (and seas) on a global and yearly scale may be viewed as the Earth's heat engine working to redistribute warm and cold air and water in an effort to lessen the significant temperature gradient between the poles and the equator.