Answer to Question #227516 in Mechanical Engineering for Unknown346307

Question

A temperature scale of certain thermometer is given by the relation

t = a ln p + b

where a and b are constants and p is the thermometric property of the fluid in the thermometer.

If at the ice point and steam point the thermometric properties are found to be 1.5 and 7.5

respectively what will be the temperature corresponding to the thermometric property of 3.5 on

Celsius scale.

Answer 1

We have:

$$0=a\ln 1.5+b,\\ 100=a\ln7.5+b.$$

Subtract one from another:

$$100=a(\ln7.5-\ln1.5)=1.609a,\\ a=62.15,\\ b=-a\ln1.5=-25.20.$$

Find the temperature corresponding to the thermometric property of 3.5 on Celsius scale:

$$t=62.15\ln3.5-25.20=52.66°\text {C}.$$