Question

Carbon dioxide gas in a piston–cylinder assembly expands from an initial state where p1 60 lbf/in.2 , V1 1.78 ft3 to a final pressure of p2 20 lbf/in.2 The relationship between pressure and volume during the process is pV1.3 constant. For the gas, calculate the work done, in Convert your answer to Btu.

Answer 1

Answer:

The amount of Work done during the process = 0.01026 BTU

Explanation:

Initial Pressure ($P_{1}$) = 60 $\frac{lbf}{in^{2} }$

Initial volume ( $V_{1}$ )= 1.78 $ft^{3}$

Final Pressure ($P_{2}$) = 20 $\frac{lbf}{in^{2} }$

Final Volume ( $V_{2}$ ) = We have to calculate.

The relationship between pressure and volume during the process is = P $V^{1.3}$

⇒ $P_{1}$ × $V_{1}^{1.3}$ = $P_{2}$ × $V_{2}^{1.3}$

⇒ $\frac{V_{2} }{V_{1} }$ = $[\frac{P_{1} }{P_{2}}]^{0.77} }$

⇒ $\frac{V_{2} }{V_{1} }$ = $3^{0.77}$

⇒ $\frac{V_{2} }{V_{1} }$ = 2.33

⇒ $V_{2}$ = 2.33 × 1.78

⇒ $V_{2}$ = 4.147 $ft^{3}$ ------------ (1)

The work done during the process is given by W = $\frac{P_{1}V_ {1}- P_{2}V_ {2} }{\gamma - 1}$

Put all the values in the above formula we get

⇒ W = $\frac{106.8 - 82.94}{1.3 - 1}$

⇒ W = 79.54 lb f

We know that 1 lb f = 0.00129 BTU

⇒ W = 0.01026 BTU

This is the amount of Work done during the process in BTU