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Question

1. Calculate the increase in volume of 5 mm3 of mercury at a temperature of 20 °C when it is heated to 50 °C. The coefficient of linear expansion of mercury is 70 x 10-6 /K. 2. A given mass of chlorine has a volume of 40 cm3 at 20 °C. Calculate its volume at 50 °C if the pressure remains constant. 3. A cylinder has a volume of 0,075 m³ and is filled with oxygen at a pressure of 380 kPa at a temperature of 50 °C. Later it is found that the pressure has dropped to 280 kPa and the temperature has decreased to 25 °C, due to a leakage. calculate the The mass of oxygen originally in the cylinder if the gas constant is 265 J/kgK. calculate the mass of oxygen that leaked if the volume of the cylinder remains constant

Answer 1

1)

Given,

Original volume of the mercury,V = 5 mm³

Initial temperature,t1 =20°C =293 K

Initial temperature,t2 =50°C =323 K

Linear expansion of mercury,α =  70 x 10^-6 /K

Calculate the  increase in volume.

ΔV = αV (t2 - t1)

     =(70 x 10^-6)(5)(323-293)

    = 0.015 mm

Therfore , the increase in volume is 0.015 mm

Answer 2

2) 

Using the ideal gas equation.

T1V1 =T2 V2

(40)(293) =(V2)(323)

V2 = (40)(293)/323 = 36.28 mm³

 

Therefore, the volume of chlorine at 50°C is 36.28 mm³

Answer 3

3)

Volume of the tank,V = 0.075 mm³

Initial pressure,P1 =380 kPa =380000 Pa

Initial temperature,t1 =50°C =323 K

Gas constant,R =  265 J/kgK.

Calculate the  mass by using the ideal gas equation.

P1V1 =m1RT1

(380000)(0.075)= m1(265)(323)

m1 =0.333 kg

Therefore, the original mass of oxygen is 0.333 kg

Answer 4

After the leaking the oxygen:

Final pressure,P2 =280 kPa =280000 Pa

Final temperature,t2 =25°C =298 K

Calculate the leaked mass by using the ideal gas equation.

P2V2 =m2RT2

(280000)(0.075)= m2(265)(298)

m2 =0.266 kg

Leaked mass,mleak = m1-m2 =0.333-0.266 =0.0267 kg

Therefore, the mass of oxygen that leaked is 0.0267 kg