Answer:
Work W=4.16 Btu
Heat transfer Q=14.56 Btu
Explanation:
To calculate the work W we will use the given pressure p=30 psia and volume V₁=0.75 ft³ V₂=2.V₁
[tex]W=p.(V_{2}-V_{1} )\\W=30psia.(1.5ft^{3}-0.175ft^{3} ).\frac{144in^{2} }{1ft^{2} } .\frac{1Btu}{778lbf.ft}\\ W=4.16Btu[/tex]
Now for heat transfer
[tex]Q=W+m.(u_{2}-u_{1} )\\Q=W+\frac{m.R.(T_{2}- T_{1})}{k-1}\\[/tex]
The last equation we will rewrite using ideal gas law to calculate heat transfer
[tex]Q=W+\frac{p(V_{2}-V_{1} )}{k-1}\\ As\\W=p(V_{2}-V_{1} )\\So\\Q=W+\frac{W}{k-1} \\Q=4.16Btu+\frac{4.16Btu}{1.4-1} \\Q=14.56Btu[/tex]
