The resistance of a platinum thermometer is 18ohms at ice point,40ohms at steam point and 34.5ohms on a certain hot day.what is the temperature of the day on celsius temperature scale
To find the temperature of the day on the Celsius temperature scale, we can use a linear equation that relates the resistance of the platinum thermometer to the temperature.
First, we need to determine the relationship between resistance and temperature using the given data.
1. Determine the temperature difference between the ice and steam points:
ΔR = R(steam) - R(ice)
ΔR = 40Ω - 18Ω
ΔR = 22Ω
2. Determine the temperature difference between the ice point and the hot day:
ΔR_day = R(day) - R(ice)
ΔR_day = 34.5Ω - 18Ω
ΔR_day = 16.5Ω
3. Determine the temperature difference per ohm:
ΔT/ΔR = ΔT_day/ΔR_day
Now, substitute the values into the equation:
ΔT/22Ω = ΔT_day/16.5Ω
Cross multiply:
ΔT * 16.5Ω = ΔT_day * 22Ω
Simplify:
16.5ΔT = 22ΔT_day
Now, we need to find the temperature difference between the hot day and the ice point.
4. Determine the temperature difference on the Celsius scale:
ΔT_day = ΔT_hot - ΔT_ice
Substitute the known values:
16.5ΔT = 22(ΔT_hot - 0°C)
Simplify:
16.5ΔT = 22ΔT_hot
Since we are interested in the temperature on the Celsius scale, we can set ΔT_ice to 0°C.
Now, divide both sides by 16.5 to find the temperature on the hot day:
ΔT_hot = (16.5ΔT) / 22
Substitute the known values:
ΔT_hot = (16.5 * (34.5Ω - 18Ω)) / 22
Simplify:
ΔT_hot = (16.5 * 16.5Ω) / 22
Calculate:
ΔT_hot = 247.5Ω / 22
Finally, calculate the temperature on the hot day using the calculated temperature difference:
T_hot = ΔT_hot + T_ice
T_hot = (247.5Ω / 22) + 0°C
Therefore, the temperature on the hot day in Celsius is (247.5Ω / 22) + 0°C.