A centigrade and a Fahrenheit thermometer are | vedclass

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(B) The relationship between the Celsius scale $(T_C)$ and the Fahrenheit scale $(T_F)$ is given by: $\frac{T_C - 0}{100} = \frac{T_F - 32}{180}$.Init

Vedclass · Accepted Answer

$40$

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(B) The relationship between the Celsius scale $(T_C)$ and the Fahrenheit scale $(T_F)$ is given by: $\frac{T_C - 0}{100} = \frac{T_F - 32}{180}$.Initially,both thermometers are in boiling water,so the initial temperature is $T_{C,i} = 100^{\circ}C$ and $T_{F,i} = 212^{\circ}F$.When the Fahrenheit thermometer registers $T_{F,f} = 140^{\circ}F$,we find the corresponding Celsius temperature $T_{C,f}$:$\frac{T_{C,f}}{100} = \frac{140 - 32}{180}$$\frac{T_{C,f}}{100} = \frac{108}{180} = 0.6$$T_{C,f} = 60^{\circ}C$.The fall in temperature as registered by the centigrade thermometer is $\Delta T_C = T_{C,i} - T_{C,f} = 100^{\circ}C - 60^{\circ}C = 40^{\circ}C$.

$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the centigrade thermometer in $^{\circ}C$?

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