Answer:
The value of heat transfer during the process Q = - 29.49 KJ
Explanation:
Given data
[tex]P_{1}[/tex] = 50 [tex]\frac{lbf}{in^{2} }[/tex] = 344.7 k pa
[tex]V_{1} = 4 ft^{3}[/tex] = 0.113 [tex]m^{3}[/tex]
[tex]T_{1} = 200[/tex] F = 366.4 K
[tex]T_{2} = 400 F[/tex] = 477.6 K
Poly tropic index n = 1.2
gas constant for oxygen = 0.26 [tex]\frac{KJ}{kg K}[/tex]
From ideal gas equation
[tex]P_{1}[/tex] [tex]V_{1}[/tex] = m R [tex]T_{1}[/tex]
Put all the values in above equation we get
⇒ 344.7 × 0.113 = m × 0.26 × 366.4
⇒ m = 0.408 kg
Heat transfer in poly tropic process is given by
Q = [tex]\frac{\gamma - n}{( \gamma - 1)( n - 1)} [ {m R (T_{1} - T_{2} ) ][/tex]
Put all the values in above formula we get
⇒ Q = [tex]\frac{1.4 - 1.2}{( 1.4 - 1)( 1.2 - 1)} [ {m R (T_{1} - T_{2} ) ][/tex]
⇒ Q = 2.5 × 0.408 × 0.26 × ( 366.4 - 477.6 )
⇒ Q = - 29.49 KJ
This is the value of heat transfer during the process & negative sign shows that heat is lost during the process.
