A temperature transducer is used to measure the temperature of steam coming out of a steam generator. The following data are available from the manufacturer of the temperature transducer:

Range: 0-1000 K

Sensitivity: of full scale

Linearity: of full scale

Accuracy: of full scale

To determine the repeatability of the transducer, 10 auxiliary tests at the desired average temperature of 800 K were run. The standard deviation of these measurements is 25 K. In a separate test of the data transmission system, 10 tests of the same temperature input resulted in a standard deviation of 20 K. The A/D converter is tested 10 times resulting a standard deviation of 15 K.

1. (10) Calculate the random uncertainty of the temperature measurement at 95% confidence level.
2. (8) Calculate the systematic uncertainty of the temperature measurement.
3. (7) Calculate the total uncertainty of the temperature measurement. If the steam temperature needs to controlled within 10% from the desired 800 K. Please comment on the adequacy of this device.

please be detailed as possible. Thank you