Question

# When 18.5 J was added as heat to a particular ideal gas, the volume of the...

When 18.5 J was added as heat to a particular ideal gas, the volume of the gas changed from 36.8 cm3 to 59.4 cm3 while the pressure remained constant at 0.944 atm. (a) By how much did the internal energy of the gas change? If the quantity of gas present is 1.38 x 10-3 mol, find the molar specific heat of the gas at (b) constant pressure and (c) constant volume.

According ot first law of thermodynamics We take heat added to the system as positive quantity and work done by the system as positive quantity,

dQ= 18.5 J

dV = 59.4-36.8 = 22.6 cm3 = 22.6 x 10-6 m3

pressure, p = 0.944 atm= 0.944 x 1.01 x 105 Pa = 0.953 x 105 Pa

(a) Change in internal energy, dU = dQ -pdV

= 18.5 - (0.953 x 105 x 22.6 x 10-6) = 18.5 - 2.15 = 16.35 J

(b), (c) We know that the specific heat capacity at constant pressure is given as

Q = nCp deltaT

Since it is an ideal gas

P1V1=nRT1

P2V2=nRT2

delta T = T2 - T1 = (P/nR) (V2-V1) = 187.8 K

Cp = (Q/n delta T) Cp = Cv +R

Cv = Cp -R

Cv = 71.3-8.314 = 62.98 J/mol K

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