# Heat required at constant pressure

#### Amith2006

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?

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#### AlephZero

Homework Helper
Because your C(p) = 709.7 can't possibly be right. If the components have Cp of 28.59 and 20.72, the mixture must have Cp in between those values.

The equation looks OK, so I guess you hit the wrong buttons on your calculator.

#### Amith2006

U r right. What am I doing??Thanks.