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Question

An ideal gas expands from  100cm3to200cm3 at  a constant pressure of  2.0×105Pawhen50J of heat is supplied to it. Calculate 

(a) The change in internal energy of the gas

(b) The number of moles in the gas if the initial temperature is 300 K.

(c) The molar heat capacity  Cp at constant pressure and 

(d) The milar heat capacity  Cv at constant volume


Solution

V1=100cm8,V2=200cm8,

P = 2×105   Pa   dQ = 50 J

(a) dQ = dU + dW

50=dU+2×105

(200-100) ×106

50=dU+2×10

  dU = 30 J.

(b)   30 = n ×32×8.3×300

[U = 32 nRt for monoatimoc ]

n=2(83×3)=2249=0.008

(c)  dU = nCvDT

 cv=dUndT=300.008×300=12.5

Cp=cv+R=12.5+8.3=20.8

(d)  Cv = 12.5

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