Question

Helium in a cylinder with a piston and initially at 23 ∘C expands at constant atmospheric pressure.

Part A

What is the work that the piston does on the gas if the air expands from 0.030 m3 to 0.041 m3 ?

Express your answer to two significant figures and include the appropriate units.

Part B

How many moles of gas are in the container?

Express your answer using two significant figures.

Part C

Suppose that the work leads to a corresponding change in thermal energy (there is no heating). What is the final temperature of the gas?

Express your answer using three significant figures.

Answer 1

(a) To calculate the work done by the on the gas. W = _P Delta V = -1(1.0 times 10^50(0.041 m^3 - 0.030 m^3) = -1100 J Therefore workdone by on the gas as equal to -110 J (b) Number of moles of the gas n = Pv/RT n = 1.221 mol (c) The final temp of the gas Delta YU_thermal = 3/2 nR Delta T = 3/2 nR (T_f - T_i) T_f = T_i + 2 Delta U_thrmal/3nR T_i = 296 K, Delta U_thermal = -1100 J, n = 1.221 rnd R = 8.3 J/mol K T_f = 296J + 2(-1100J)/3(1.22 1 mol)(8.3J/mol.k) T_f = 223 K