Question

The temperatures of two bodies measured by a thermometer are $t_1={20}^{o}C\pm {0.5}^{o}C$ and $t_2={50}^{o}C\pm {0.5}^{o}C$. The temperature difference and the error there is

• A. ${30}^{o}C\pm 1^{o}C$
• B. ${70}^{o}C\pm {0.5}^{o}C$
• C. ${30}^{o}C\pm {0.5}^{o}C$
• D. ${70}^{o}C\pm 1^{o}C$

Answer 1

The correct option is A ${30}^{o}C\pm 1^{o}C$

$\text{Step 1: Calculate temperature difference}$

Given: $t_1={20}^{o}C\pm {0.5}^{o}C$ $....\left(1\right)$

$t_2={50}^{o}C\pm {0.5}^{o}C$ $....\left(2\right)$

$T_{diff}=t_2-t_1$

Using equation (1) and (2) we get

$T_{diff}={50}^{o}C-{20}^{o}C={30}^{o}C$

$\text{Step 2: Error Calculation}$

Also, error in $T_{diff}$ will be equal to sum of errors in $t_1$ and $t_2$

$\therefore \Delta T_{diff}=\Delta t_1+\Delta t_2$

From equation $\left(1\right)$ and $\left(2\right)$: $\Delta t_1={0.5}^{o}C$ and $\Delta t_2={0.5}^{o}C$

$\Rightarrow \Delta T_{diff}={0.5}^{o}C+{0.5}^{o}C=1^{o}C$

$\Rightarrow T_{diff}={30}^{o}C\pm 1^{o}C$

Hence option $A$ is correct.