Question

Five moles of monatomic ideal gas are contained at a pressure of 4 atm and a temperature of 250 K. 35400 J of heat are transferred to the gas. Then, the gas pressure is used to expand a piston, and the expanding gas does 1200 J of work against its surroundings. However, the piston is not perfectly insulated, and 600 J of heat is lost from the gas during the expansion. All processes are reversible. Calculate the final temperature of the gas.

Answer 1

Moles of Gas = 5

Pressure = 4 atmosphere

Temperature = 250 K

Q = 35400 J

The work done by the gas = 1200J

Heat loss = 600 J

a) Initial temperature = 250 K

b) Heat given = 35400

Let us calcualte the temperature at this point

Q_AB = n C_VT = 35400

(n) ((3/2) R) (T) = 35400 J

(5 mole) ((3/2) 8.31 J/mole-K) (T) = 35400 J

( 62.35 J / K ) T = 35400 J

T = (500/12.5) K

T = 567.76

New temperature =250 K + 567.76 K = 817.75 K

c) For final temperature

Heat total = -600 J = n C_PT

- 600 J = (5) ((5/2) R) (T)

- 600 J = (5 ((5/2) 8.31 J/mole-K) (T)

-

T = - 5.77 K

Final tempeature = 817.75 - 5.77 = 811.9 K