Question

A platinum resistance thermometer has resistances of 160.0 when placed in a 0°C ice bath and 243.8 when immersed in a crucible containing a melting substance. What is the melting point of this substance? (Hint: First determine the resistance of the platinum resistance thermometer at room temperature, 20°C.)

Answer 1

the melting point T = 125.36°C

Step-by-step explanation:

Given that:

The resistance of a platinum thermometer at 0°C is
`R_o` = 160.0 ohms

The resistance of a platinum thermometer when immersed in a crucible containing a melting substance
`R_t` = 243.8 ohms

The temperature coefficient at room temperature 20°C = ∝ = 0.00392

The objective is to determine the melting point of this substance

To do that ; at 20°C, the resistance of the platinum thermometer can be calculated as follows:

`R_(20) = R_o(1 + \alpha \Delta T)`

`R_(20) = 160(1 + (0.00392 * (20-0)^0C))`

`R_(20) = 160(1 + (0.00392 * (20))`

`R_(20) = 160(1 + (0.0784)`

`R_(20) = 160(1.0784)`

`R_(20) = 172.544 \ ohms`

The resistance of the platinum thermometer at t°C ,
`R_t` =
`R_(20)(1 + \alpha \Delta T)`

`243.8 = 172.544(1 + 0.00392 * (T-20)^0C}`

`(243.8)/( 172.544 )= (1 + 0.00392 * (T-20)^0C}`

`1.413 = (1 + 0.00392 * (T-20)^0C}`

`1.413-1 = 0.00392 * (T-20)^0C}`

`0.413 = 0.00392 * (T-20)^0C}`

`(0.413 )/(0.00392) = (T-20)^0C}`

105.36°C = (T - 20) °C

T = 105.36°C + 20 °C

T = 125.36°C