2.4 kg of nitrogen at an initial state of 285K and 150 kPa is compressed slowly in an isothermal process to a final pressure of
1 answer:
Answer:
W=-280.67 KJ
Explanation:
Given that
Initial pressure = 150 KPa
Final pressure = 600 KPa
Temperature T= 285 K
Mass m=2.4 Kg
We know that ,work in isothermal process given as
Gas constant for nitrogen gas R=0.296 KJ/kgK
Now by putting the values
W=-280.67 KJ
Negative sign indicates that it is compression process and work is done on the gas.
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This question is not complete, the complete question is;
A thin-walled pressure vessel 6-cm thick originally contained a small semicircular flaw (radius 0.50-cm) located at the inner surface and oriented normal to the hoop stress direction. Repeated pressure cycling enabled the crack to grow larger. If the fracture toughness of the material is , the yield strength equal to 1250 MPa, and the hoop stress equal to 300 MPa, would the vessel leak before it ruptured
Answer:
length of crack is 5.585 cm
we will observe that, the length of crack (5.585 cm) is less than the vessel thickness (6 cm) Hence, vessel will not leak before it ruptures
Explanation:
Given the data in the question;
vessel thickness = 6 cm
fracture toughness k =
yield strength = 1250 MPa
hoop stress equal = 300 MPa
we know that, the relation between fracture toughness and crack length is expressed as;
k = (1.1)(2/π)(r√(πa))
where k is the fracture toughness, r is hoop stress and a is length of crack
so we rearrange to find length of crack
a = 1/π[( k / 1.1(r)(2/π)]²
a = 1/π[( kπ / 1.1(r)(2)]²
so we substitute
a = 1/π [( 88π / 1.1(300)(2/π)]²
a = 1/π[ 0.1754596 ]
a = 0.05585 m
a = 0.05585 × 100 cm
a = 5.585 cm
so, length of crack is 5.585 cm
we will observe that, the length of crack (5.585 cm) is less than the vessel thickness (6 cm) Hence, vessel will not leak before it ruptures