A measuring cylinder made of glass has a volume of 200 mL when measured at 20°C....

A measuring cylinder made of glass has a volume of 200 mL when measured at 20°C. Mercury, also at 20°C, is added to the measuring cylinder until the mercury level reads 197 mL on the measuring cylinder scale. The mercury and glass are then warmed until the mercury level reads 200 mL on the measuring cylinder scale. Taking the coefficients of volume expansion of glass to be 2.0 × 10^-5 K^-1 and for mercury to be 18 × 10^-5 K^-1, what is the final temperature?

Expert Solution

Note that the coefficient of volume expansion of glass is much smaller than that of mercury. So, it is a good approximation to ignore changes in the measuring cylinder and find the final temperature by considering the expansion of only mercury. With this approximation we need to find the increase in temperature so that the volume of mercury increases from 197 mL to 200 mL.

Change in volume of mercury is

Coefficient of volume expansion is fractional change in the volume per unit change in the temperature. So,

Therefore

The value of in is same as the value of in Kelvin .

Therefore, final temperature is about 104.6 degree Centigrade.

genius_generous answered 2 years ago

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