EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
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Chapter 20, Problem 33P

(a)

To determine

To Calculate:The temperature at which water boils on mountain.

(a)

Expert Solution
Check Mark

Answer to Problem 33P

  90°C

Explanation of Solution

Given:Atmospheric pressure 70.0 kPa .

Formula used:

Clausius-Clapeyron equation is

  ln(P2P1)=(ΔHvapR)(1T1-1T2)

Here, P2 is the final pressure, P1 is the initial pressure, ΔHvap is the enthalpy of vaporization ofwater, R is the universal gas constant, T is the boiling temperature of the water, and ΔT is thevariable temperature.

Calculation:

Rewrite the equation,

ln(P2P1)=(ΔHvapR)(1T1-1T2) for T2

  1T1-1T2=ln( P2 P1)(R ΔHvap)1T2=1T1-ln( P2 P1)(R ΔHvap)T2=1[ 1 T 1 -( ln( P2 P1 )( R ΔHvap ))]

The boiling point of the water is 100°C and the atmospheric pressure is 1atm .

Covert Celsius temperature to Kelvin temperature as follows:

  T1 = (100 + 273)KT1 = 373K

Substitute 373 K = T1, 70.0 kPa =P2, 1 atm = P1, 8.314J/mol.K= R, 40.66×109J/mol=ΔHvap in the equation

  T2=1[1 T 1-(ln( P2 P1 )( R ΔHvap ))]

P, R and solve for T

T2=1[1373K-(ln( 70.0kPa 1atm( 101.325kPa 1atm ) )( 8.314J/mol×K 40 .66×10 3 J/mol ))]T2= 363.0 K

Covert Kelvin temperature to Celsius temperature as follows:

  T2 = (363– 273)°CT2 = 90°C

Conclusion: Therefore, the temperature at which the water boils on the mountain is 90°C .

(b)

To determine

To Calculate:The temperature at which water boils in a container.

(b)

Expert Solution
Check Mark

Answer to Problem 33P

   81°C

Explanation of Solution

Given: pressure 0.500 atm

Calculation: The water boils inside the container and the pressure inside the container is 0.500 atm .

The temperature, where the water boils in a container is,

T2=1[1 T 1-(ln( P2 P1 )( R ΔHvap ))]

Substitute 373 K =T1, 0.500 atm = P2, 1 atm = P1, 8.314J/mol K = R, and T240.66x10J/mol = ΔHvap in the equation

T2=1[1 T 1-(ln( P2 P1 )( R ΔHvap ))] to solve T2

T2=1[ 1 373K -( ln( 0.500atm 1atm )( 8.314J/mol.K 40 .66×10 3 J/mol ))]T2, = 355K

Covert Kelvin temperature to Celsius temperature as follows:

  T2 =(354– 273)°CT2 = 81°C

Therefore, the temperature at which the water boils in the container is  81°C

Conclusion: By usingClausius-Clapeyron equation,the temperature at which the water boils in the container can be calculated.

(c)

To determine

To Calculate:The pressure at water boils at 115°C is to be calculated.

(c)

Expert Solution
Check Mark

Answer to Problem 33P

  170 kPa

Explanation of Solution

Given: Temperature 115°C .

Calculation:The Clausius-Clapeyron equation is

  ln(P2P1)=(ΔHvapR)(1T1-1T2)

Apply anti-logarithm to the above equation on both sides

  ( P2 P1)=e( ΔHvap R )( 1 T 1 - 1 T 2 )P2=P1e( ΔHvap R )( 1 T 1 - 1 T 2 )

Covert Celsius temperature to Kelvin temperature as follows:

P2=P1e( ΔHvapR)(1 T 1 -1 T 2 )

  T1 = (115 + 273)KT1 = 388K

Substitute

   373 K =T1, 388 K = T2,1 atm = P1, 8.314J/mol. K = R,40.66×103 J/mol = ΔHvap in the equation and solve for P2.

  P2=(1atm)e( 40 .66×10 3 J/mol 8.314J/molK )( 1 373K - 1 388K )P2=(1atm( 101.33kPa 1atm ))e( 40 .66×10 3 J/mol 8.314J/molK )( 1 373K - 1 388K ) P2 = 168.23 kPaP2 170 kPa

Therefore, the pressure at which the water boils at 115°C temperature is 170 kPa.

Conclusion:Bythe Clausius-Clapeyron equation, the pressure at which the water boils at 115°C temperature can be calculated.

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