Question

A piston-cylinder assembly contains air at a pressure of 30 lbf/in2 and a volume of 0.75 ft3. The air is heated at constant pressure until its volume is doubled. Assuming the ideal gas model, with constant specific heat ratio of k=1.4 for the air, determine the work and heat transfer, each in BTU.

Answer 1

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

$W=p.(V_{2}-V_{1} )\\W=30psia.(1.5ft^{3}-0.175ft^{3} ).\frac{144in^{2} }{1ft^{2} } .\frac{1Btu}{778lbf.ft}\\ W=4.16Btu$

Now for heat transfer

$Q=W+m.(u_{2}-u_{1} )\\Q=W+\frac{m.R.(T_{2}- T_{1})}{k-1}$

The last equation we will rewrite using ideal gas law to calculate heat transfer

$Q=W+\frac{p(V_{2}-V_{1} )}{k-1}\\ As\\W=p(V_{2}-V_{1} )\\So\\Q=W+\frac{W}{k-1} \\Q=4.16Btu+\frac{4.16Btu}{1.4-1} \\Q=14.56Btu$