Answer to Question #305381 in Molecular Physics | Thermodynamics for Tobias Felix

Question

How much work is necessary to compress air in an insulated cylinder from 0.20 to 0.01

m3

. Use T1= 20C and P1= 100Kpa

Answer 1

Assuming the process to be adiabatic, the work can be found as follows (see https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/03%3A_The_First_Law_of_Thermodynamics/3.07%3A_Adiabatic_Processes_for_an_Ideal_Gas):

$$W = \dfrac{p_2V_2-p_1V_1}{1-\gamma}$$

where $p_1 = 10^5Pa,V_1 = 0.2m^3,V_2=0.01m^3,\gamma=1.4$ and $p_2$ is the final pressure. From the adiabatic relation, the final pressure is given as follows:

$$p_2 = p_1( \dfrac{V_1}{V_2})^\gamma = 10^5\cdot \dfrac{0.2^{1.4}}{0.01^{1.4}} \approx 66.29\times 10^5Pa$$

Thus, obtain:

$$W = \dfrac{66.29\times 10^5\cdot 0.01 - 10^5\cdot 0.2}{1-1.4} \approx -1.2\times 10^5J$$

Answer. $-1.2\times 10^5J$