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**1. Homework Statement**

1) How much heat energy must be added to the gaseous mixture consisting of 1 gm of Hydrogen and 1 gm of Helium to raise its temperature from 0 degree C to 100 degree C

at constant pressure? Given that g1=1.41, g2=1.67

**2. Homework Equations**

Heat required = nC(p)dT

**3. The Attempt at a Solution**

Heat energy in Joules:

Let C(p1), C(p2) and C(p) be the specific heat of Hydrogen, Helium and the mixture at constant pressure respectively. Let g1,g2 and g be the ratio of the specific heats at constant volume and pressure for Hydrogen, Helium and the mixture respectively. Here I have taken the value of the universal Gas constant[R] = 8.314 Joule/mole-K

C(p1) = (g1 x R)/(g1 -1)

= 28.59 J/mole-K

C(p2) = (g2 x R)/(g2-1)

= 20 .72 J/mole-K

C(p) = {(n1 x C(p1)) + (n2 x C(p2))}/(n1 + n2)

= 709.7 J/mole-K

Let n1,n2 and n be the number of moles of Hydrogen, Helium and the mixture respectively.

n1 = 0.5 moles

n2 = 0.25 moles

n = 0.75 moles

Heat required = nC(p)dT

= 53200 Joules = 12666 Calories

Heat energy in Calories:

Here I have taken the value of the universal Gas constant[R] = 1.99 Calorie/mole-K

Heat required = 466 Calories

Why do I get 2 different answers just because of change in units of R?