The resistance Rt of a platinum varies with a temperature t according to the equation Rt=R0(1+8000bt-btsquare) calculate the temperature on platinum scale corresponding to 400 centigrade ?

To calculate the temperature on the platinum scale corresponding to 400 degrees Celsius, we need to first convert the temperature from Celsius to Kelvin.

Given:
t = 400 degrees Celsius
R0 = resistance at 0 degrees Celsius
b = coefficient

To convert Celsius to Kelvin, we use the formula:
T(K) = t(°C) + 273.15

So, the temperature in Kelvin would be:
T = 400 + 273.15
T = 673.15 K

Now, we can substitute the values into the equation:
Rt = R0(1 + 8000bT - bT^2)

Rt = R0(1 + 8000b(673.15) - b(673.15)^2)

Now, we need to solve for Rt using the given equation and the values we have calculated.

Given:

- Resistance equation: Rt = R0(1 + 8000bt - bts²)
- R0 = Resistance at 0°C
- b = Temperature coefficient of resistance (for platinum: 0.0039)
- t = Temperature in °C
- Rt = Resistance at 400°C = ?

Steps:

1. Convert temperature to the platinum scale:

The platinum scale is defined by the equation:

```
t_pt = t_c / 1.5
```

where:

- t_pt is the temperature on the platinum scale
- t_c is the temperature on the Celsius scale

Therefore, for 400°C:

```
t_pt = 400°C / 1.5 = 266.67°Pt
```

2. Substitute t and b into the resistance equation:

```
Rt = R0(1 + 8000bt - bts²)
```

```
Rt = R0(1 + 8000(0.0039)t_pt - (t_pt)²)
```

3. Solve for Rt:

```
Rt = R0(1 + 8000(0.0039)(266.67) - (266.67)²)
```

```
Rt = R0(1 + 20.67 - 70920.78)
```

```
Rt = R0(-70900.11)
```

Therefore, the resistance of the platinum at 400°C is -70900.11R0.

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