volume temperature mass

Question

7.2 A steel plate has a volume of 4,37 m3 at a temperature of 20 °C and has to be enlarged to a volume of 4,5 m 3. The steel plate has a linear coefficient of expansion of 1,5 x 10 4/0C. Calculate to what temperature the steel plate must be heated to achieve the new volume. 7.3 A cylinder has a capacity of 0,075 m3 and is filled with oxygen at a pressure of 380 kPa and a temperature of 50 °C. Later it is found that owing to a leak, the pressure has dropped to 280 kPa and the temperature has decreased to 25 °C. Calculate the following: 7.3.1 The mass of the oxygen that was initially in the cylinder if the gas constant is 265 J/kgK 7.3.2 The mass of oxygen that leaked out if the volume of the cylinder is kept constant

Answer 1

(7.2)

The volume of the steel plate = 4.37 m³.

Temperature = 20°C.

The Enlarged volume = 4.5 m³.

Linear coefficient of expansion = 1.5 * 10^-4

Then Volume coefficient of expansion  = 3*(Linear coefficient of expansion)

Volume coefficient of expansion = 3 * 1.5 * 10^-4

Volume coefficient of expansion = 4.5 * 10^-4.

Therefore the temperature of the volume = 26.61°C.

Answer 2

(7.3.1)

The Volume of the cylinder = 0.075 m³.

Pressure of the Oxygen  = 380 kPa.

Temperature = 50°C = 50+273 = 323 K

Gas Constant R = 256 J/kg - K.

The ideal gas Equation is

PV = mRT

m = (PV) / RT

m = (380 * 10³ * 0.075) / (256 * 323)

m = 0.344 kg

Mass of the oxygen = 0.344kg.

Answer 3

(7.3.2)

The Volume of the cylinder = 0.075 m³.

Pressure of the Oxygen  = 380 kPa.

Temperature = 50°C = 50+273 = 323 K

Gas Constant R = 256 J/kg - K.

The ideal gas Equation is

PV = mRT

m = (PV) / RT

m = (380 * 10³ * 0.075) / (256 * 323)

m = 0.344 kg

Mass of the oxygen = 0.344kg.

Reduced Pressure of the Oxygen  = 280 kPa.

Reduced Temperature = 25°C = 25+273 = 298 K

The ideal gas Equation is

PV = mRT

m = (PV) / RT

m = (280 * 10³ * 0.075) / (256 * 298)

m = 0.275 kg

Mass of Oxygen after getting leaked = 0.275 kg.

Amount of oxygen leaked = 0.344 - 0.275 = 0.068 kg

Amount of oxygen leaked = 0.068 kg.