Answer to Question #299238 in Molecular Physics | Thermodynamics for Ama SuPa

Question

 

a) 0.056m³ of air at 1.38 bar are compressed isothermally to a volume of 0.014m³. 

Determine the work energy required for the compression.

b) compare this to the work energy which would be required for an adibatic compression through the same volume ratio. For air R= 0.287KN and ➰ = 1.4

Answer 1

Given:

$V_1=0.056\:\rm m^3$

$V_2=0.014\:\rm m^3$

$p_1=1.38*10^5\:\rm Pa$

(a) $T=const$

$$W=p_1V_1\ln\frac{V_2}{V_1}$$

$$W=1.38*10^5*0.056\ln\frac{0.014}{0.056}=-10713\:\rm J$$

(b) $\delta Q=0$

$$W=\frac{p_1V_1((\frac{V_2}{V_1})^{1-\gamma}-1)}{1-\gamma}$$

$$W=\frac{1.38*10^5*0.056((\frac{0.014}{0.056})^{1-1.4}-1)}{1-1.4}$$

$$W=-14318\:\rm J$$