a resistance of platinum wire is 2 ohm at zero degree and 2.5 at 100 degree.then at what temperature its resistance would be 2.3 ohm.
is the change linear? If so, then
since 2.3 is 3/5 of the way from 2.0 to 2.5,
the temperature would be 3/5 of the way from 0 to 100 degrees.
60
To find the temperature at which the resistance of the platinum wire would be 2.3 ohms, we can use the concept of temperature coefficient of resistance.
The temperature coefficient of resistance (α) is defined as the rate of change of resistance with respect to temperature. It indicates how the resistance of a material changes with temperature.
In the case of platinum, we can use the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R1 is the initial resistance at temperature T1,
R2 is the final resistance at temperature T2, and
α is the temperature coefficient of resistance for platinum.
We are given the following information:
R1 = 2 ohms (at 0 degrees Celsius)
T1 = 0 degrees Celsius
R2 = 2.3 ohms (we need to find T2)
α (temperature coefficient of resistance) = (R2 - R1) / (R1 * (T2 - T1))
Let's plug in the values and solve for T2:
2.3 = 2 * (1 + α * (T2 - 0))
Rearranging the equation, we have:
α = (R2 - R1) / (R1 * (T2 - T1))
α = (2.3 - 2) / (2 * (T2 - 0))
α = 0.3 / (2 * T2)
α = 0.15 / T2
Now we can substitute this value back into the equation:
2.3 = 2 * (1 + (0.15 / T2) * (T2 - 0))
Simplifying further:
2.3 = 2 + (0.15 / T2) * (T2 - 0)
2.3 - 2 = 0.15 * (T2 - 0)
0.3 = 0.15 * T2
T2 = 0.3 / 0.15
T2 = 2
Therefore, the temperature at which the resistance of the platinum wire would be 2.3 ohms is 2 degrees Celsius.