Question 238: Thermodynamics & KTG

Question

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omega$$ and $$10 \Omega$$ respectively. After inserting in a hot bath of temperature $$400^{\circ} \mathrm{C}$$, the resistance of platinum wire is :

Accepted Answer

The resistance of a platinum resistance thermometer varies linearly with temperature. The relation can be given by:
$$R_t = R_0(1 + \alpha t)$$
where:
$$R_t$$ is the resistance at temperature $$t$$,
$$R_0$$ is the resistance at 0ÃÂ°C (ice point),
$$\alpha$$ is the temperature coefficient of resistance, and
$$t$$ is the temperature in degrees Celsius.
In this question, we are given:
Resistance at the ice point ($$R_{0} = 8 \Omega$$),
Resistance at the steam point ($$R_{100} = 10 \Omega$$).
To find the temperature coefficient of resistance ($$\alpha$$), we use the resistance values at the ice and steam points:
$$\alpha = \frac{R_{100} - R_0}{R_0 	imes 100} = \frac{10\Omega - 8\Omega}{8\Omega 	imes 100} = \frac{2\Omega}{800\Omega} = \frac{1}{400} 	ext{ per } ^{\circ}C$$
Now, to find the resistance $$R_t$$ at $$400 ^{\circ}C$$, we substitute $$\alpha$$, $$R_0$$, and $$t = 400$$ into the formula:
$$R_t = R_0(1 + \alpha t) = 8\Omega(1 + \frac{1}{400} 	imes 400) = 8\Omega(1 + 1) = 8\Omega 	imes 2 = 16\Omega$$
Hence, the resistance of the platinum wire at $$400^{\circ}C$$ is $$16 \Omega$$. The correct option is:
Option B: 16 $$\Omega$$

Answer

10 $$\Omega$$

Answer

16 $$\Omega$$

Answer

8 $$\Omega$$

Answer

2 $$\Omega$$

Thermodynamics & KTG

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega and 10 \Omega respectively. After inserting in a hot bath of temperature 400^{\circ} \mathrm{C}$, the resistance of platinum wire is :

Choose the correct answer: