(a) Find the work done on the environment. J (b) Find the change in internal ene

Question

(a) Find the work done on the environment.
J

(b) Find the change in internal energy of the gas.
J

(c) Use the First Law of Thermodynamics to obtain the thermal energy absorbed by the gas during the process.
J

(d) Use the molar heat capacity at constant pressure to find the thermal energy absorbed.
J

(e) How would the answers change for a diatomic ideal gas?

EXERCISE

(a) Find the work done on the gas.
Wg =  J

(b) Find the change in internal energy.
U =  J

(c) Find the energy transferred by heat, Q.
Q =  J

Explanation / Answer

P = pressure = 2.45 x 105 Pa

Vi = initial Volume = 1.04 L = 1.04 x 10-3 m3

Vf = final volume = 2.50 L = 2.50 x 10-3 m3

Change in volume, V = Vf - Vi = (2.50 x 10-3 ) - (1.04 x 10-3) = 1.46 x 10-3 m3

Initial Temperature = Ti = 293 K

a)

Work done is given as ::

W = P V = (2.45 x 105) (1.46 x 10-3) = 357.7 J

b)

Tf = final temperature

using the formula

Vi/Ti = Vf/Tf

(1.04 x 10-3 )/ 293 = (2.50 x 10-3) / Tf

Tf = 704.33 K

Change in Temperature = T = Tf - Ti = 704.33 - 293 = 411.33 K

using the formula

PVi = n R Ti

n = number of moles = (2.45 x 105) (1.04 x 10-3) / (8.314 x 293) = 0.105

internal energy change is given as :

U = (3/2) n R T

U = 1.5 x 0.105 x 8.314 x 411.33 = 538.62 J

c)

Using first law of thermodyanamics

Q = U + W

Q = 538.62 + 357.7

Q = 896.32 J

d)

Q = (5/2) nR T

Q = 2.5 x 0.105 x 8.314 x 411.33

Q = 897.7 J

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