Question

A cylinder of monatomic ideal gas is sealed in a cylinder by a piston. Initially, the gas occupies a volume of 3.00 L and the pressure is initially 105 kPa. The cylinder is placed in an oven that maintains the temperature at a constant value. 65.0 J of work is then done on the piston, compressing the gas (in other words, the gas does −65.0 J of work). The work is done very slowly so that the gas maintains a constant temperature. You should sketch this process on a P-V diagram, to get an idea about what is going on.

(a) Find the change in internal energy of the gas in this process.

(b) Find the final volume occupied by the gas.

(c) Find the final pressure of the gas.

Answer 1

given P1 = 105000 Pa = 105000N/m2

V1 = 3 L = 3 x10^-3 m3

so T1 = P1V1 /nR = (105000) x (3 x10^-3)/ 8.314 = 37.88 degree c

as isothermal so T2 = T1 = 37.88 degree C

in isothremal work done W = P1 V1 x ln(V2/V1) = 105000 x0.003 x ln (V2/3)

as W = 65 J

105000 x0.003 x ln (V2/3) = 65

so V2 = 3.68 L ...........asnwer (b)

c) as isothermal

P1 V1 = P2 V2

105 x 3 =P2x 3.68

P2 = 85.42 kPa ...............(c)

a) as T = 0 ( isothermal)

so U = m C T

U = 0.................(a)