Question

The temperature of two bodies as measured by a thermometer are ${{t}_{1}}=20\pm {{0.5}^{o}}C$ and ${{t}_{2}}=50\pm {{0.5}^{o}}C$. The temperature difference and error there is-
(A). $30\pm {{1}^{o}}C$
(B). $70\pm {{0.5}^{o}}C$
(C). $30\pm {{0.5}^{o}}C$
(D). $70\pm {{1}^{o}}C$

Answer 1

Hint: Two bodies are at different temperatures and their measurements have little uncertainty. The difference of temperature between their bodies will add up the uncertainties. Therefore, while the temperatures get subtracted their uncertainties get added.
Formulas used:
$T={{t}_{2}}-{{t}_{1}}$
$\Delta t=\Delta {{t}_{1}}+\Delta {{t}_{2}}$

Complete answer:
The temperature of a body is the measure of its hotness or coldness. Its SI unit is K.
The error in the measurement of a quantity is known as absolute error.
The uncertainty in measurement of a quantity is the error which can occur in its measurement. For example in measurement of temperature, ${{t}_{1}}=20\pm {{0.5}^{o}}C$, $\pm 0.5$ is the uncertainty.
The uncertainty in a measurement depends upon the precision. Precision is a measure of how reliable and well a result is.
Given temperatures of two bodies as ${{t}_{1}}=20\pm {{0.5}^{o}}C$ and ${{t}_{2}}=50\pm {{0.5}^{o}}C$.
The temperature difference between the two bodies is-
$\begin{align}
  & T={{t}_{2}}-{{t}_{1}} \\
 & \Rightarrow T=50-20 \\
 & \Rightarrow T={{30}^{o}}C \\
\end{align}$
The temperature difference between the two bodies is ${{30}^{o}}C$. The error in the calculation of the temperature will be-
$\Delta t=\Delta {{t}_{1}}+\Delta {{t}_{2}}$
From the above equation, we can say that the uncertainties get added.
Given, $\Delta {{t}_{1}}={{0.5}^{o}}$ and $\Delta {{t}_{2}}={{0.5}^{o}}$. We substitute given values in the above equation to get,
$\begin{align}
  & \Delta t=0.5+0.5 \\
 & \Rightarrow \Delta t={{1}^{o}}C \\
\end{align}$
The temperature difference and error will be- $30\pm {{1}^{o}}C$.
Therefore, the temperature difference and error in it is $30\pm {{1}^{o}}C$.

Hence, the correct option is (A).

Note:
The heat flows from a higher temperature to a lower temperature. Uncertainty is an error that may or may not occur in the measurement. There are different types of errors like percentage error, relative error etc. The errors in measurements can be caused due to many factors like parallax, environmental factors, instrument calibration etc.