Question

The resistance in ohms of a metal wire temperature sensor varies directly as the temperature in degrees Kelvin (K). If the resistance is 600 ohms at a temperature of 150 K, find the resistance at a temperature of 260 K. The resistance at a temperature of 260 K is ____ ohms.

Answer 1

By determining the constant of proportionality from the given data (600 ohms at 150 K), we calculate the resistance at 260 K to be 1040 ohms, since resistance varies directly with temperature.

Step-by-step explanation:

The resistance in ohms of a metal wire temperature sensor varies directly as the temperature in degrees Kelvin. Since the resistance at 150 K is given as 600 ohms, we can write this direct variation as R = kT, where 'R' is the resistance, 'T' is the temperature in Kelvin, and 'k' is the constant of proportionality. To find 'k', we use the given information:

600 = k(150)

Which gives us k = 600 / 150 = 4.

Now, to find the resistance at a temperature of 260 K, we substitute 'k' and the new temperature into the direct variation equation:

R = 4(260)

R = 1040 ohms.

So the resistance at a temperature of 260 K is 1040 ohms.