Question

The resistance in ohms of a metal wire temperature sensor varies directly as the temperature in degrees Kelvin​ (K). If the resistance is 510 ohms at a temperature of 170 ​K, find the resistance at a temperature of 250 K?

Answer 1

Answer:

The resistance at a temperature of 250 K is 750 ohms

Step-by-step explanation:

We know that the resistance of a metal wire temperature sensor varies directly as the temperature, so we can construct a model using direct variation.

The definition of direct variation is:

Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that

$y=kx$

The number k is called the constant of proportionality.

Applying the definition of direct variation to our situation, we get

Let R be the resistance in ohms, and t the temperature in K

$R=kt$

Next, find the value of k, we know that when the temperature is 170 K the resistance is 510 ohms

$510=k\cdot 170\\\\k=\frac{510}{170}=3\:\frac{ohms}{K}$

Substitute k into the equation

$R=3\cdot t$

Find the resistance at a temperature of 250 K

$R=3\cdot 250=750 \:ohms$

The resistance at a temperature of 250 K is 750 ohms.