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VLD [36.1K]
4 years ago
10

Two common materials we encounter in our daily lives are radiator coolant in automobiles and dry ice. The coolant in an automobi

le radiator, a solution of antifreeze (a glycol such as ethylene or propylene glycol) and water, freezes at 39°C and boils at 110°C. The temperature of the dry ice (solid carbon dioxide) used in some ice cream vending carts is –78°C. Convert the boiling point of radiator coolant (110°C) to degrees Fahrenheit. Convert the temperature of dry ice (–78°C) to the Kelvin scale.
Chemistry
1 answer:
Yuki888 [10]4 years ago
3 0

Answer:

See explanation

Explanation:

Using the formula

°C = (F-32) × 5/9

Where;

°C = temperature in degrees centigrade

F= temperature in Fahrenheit

F= (9/5 ×°C) +32

F= (9/5 × 110) + 32

F= 230°F

To convert -78°C to Kelvin

-78°C + 273 = 195 K

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Answer:

The coefficient of thermal expansion α is  

      \alpha  =  \frac{1}{T}

The coefficient of compressibility

      \beta   =  \frac{1}{P}

Now  considering (\frac{ \delta P }{\delta  T} )V

From equation (1) we have that

       \frac{ \delta P}{\delta  T}  =  \frac{n R }{V}

From  ideal equation

         nR  =  \frac{PV}{T}

So

     \frac{\delta P}{\delta  T}  =  \frac{PV}{TV}

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=>   \frac{\delta  P}{\delta  T}  =  \frac{\alpha }{\beta}

Explanation:

From the question we are told that

   The  coefficient of thermal expansion is \alpha  =  \frac{1}{V} *  (\frac{\delta V}{ \delta  P})  P

    The coefficient of compressibility is \beta  =  - (\frac{1}{V} ) *  (\frac{\delta V}{ \delta P} ) T

Generally the ideal gas is  mathematically represented as

        PV  =  nRT

=>      V  =  \frac{nRT}{P}  --- (1)

differentiating both side with respect to T at constant P

       \frac{\delta V}{\delta T }  =  \frac{ n R }{P}

substituting the equation above into \alpha

       \alpha  =  \frac{1}{V} *  ( \frac{ n R }{P})  P

        \alpha  = \frac{nR}{PV}

Recall from ideal gas equation  T =  \frac{PV}{nR}

So

          \alpha  =  \frac{1}{T}

Now differentiate equation (1) above with respect to  P  at constant T

          \frac{\delta  V}{ \delta P}  =  -\frac{nRT}{P^2}

substituting the above  equation into equation of \beta

        \beta  =  - (\frac{1}{V} ) *  (-\frac{nRT}{P^2} ) T

        \beta =\frac{ (\frac{n RT}{PV} )}{P}

Recall from ideal gas equation that

       \frac{PV}{nRT}  =  1

So

       \beta   =  \frac{1}{P}

Now  considering (\frac{ \delta P }{\delta  T} )V

From equation (1) we have that

       \frac{ \delta P}{\delta  T}  =  \frac{n R }{V}

From  ideal equation

         nR  =  \frac{PV}{T}

So

     \frac{\delta P}{\delta  T}  =  \frac{PV}{TV}

=>  \frac{\delta  P}{\delta  T}  =  \frac{P}{T}

=>   \frac{\delta  P}{\delta  T}  =  \frac{\alpha }{\beta}

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