The gas, initially at 10 bar, is expanded tenfold in volume against a constant external pressure of 1 bar, all at 298 K. Calculate q, w, DU, and DH for the gas.

Respuesta :

The value of q, w, ΔU and ΔH are +2232J, -2232J, 0, 0

Data given;

  • P1 = 10bar
  • P2 = 1 bar
  • T = 298K

Ideal Gas Equation

Using ideal gas equation, we can calculate the volume

PV = nRT

  • P = pressure
  • V = volume
  • n = number of moles
  • R = ideal gas constant
  • T = Temperature

substituting the values

[tex]PV=nRT\\\\10*v = 1*8.314*10^-^5*298\\V_1= 2.48*10^-^3m^3[/tex]

The initial volume is 2.48*10^-3 m^3

However, the volume increased by 10 times.

[tex]v_2= 2.48*10^-^3*10=0.0248m^3[/tex]

Work Done

The work done(w) on the gas is

[tex]W=-p\delta V\\W= -1*(0.0248-0.00248)\\W=-0.02232barm^3\\W=-2232J[/tex]

NB; 1 bar m^3 = 1000J

ΔU

[tex]\delta U= C_v\delta T\\\\\delta U = 0[/tex]

This is an isothermal process, i.e a process that underwent no change in temperature.

Q

[tex]\delta U = Q+W\\0=Q+W\\Q= -W\\Q = -(-2232)\\Q = 2232J[/tex]

The value of Q is 2232J

ΔH

The ΔH of the gas can be calculated as

[tex]\delta H = C_p\delta T = 0[/tex]

Since there's no change in temperature, ΔH = 0

From the calculations above, the value of q, w, ΔU and ΔH are +2232J, -2232J, 0, 0

Learn more on work done on a gas and isothermal process here;

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