# A cylinder of fixed capacity 67.2 litres contains helium gas at st.p.the amount of heat required to raise the temperature of the gas by 15 degree celsius is(R=8.31 j/mol/k) a.520j b.560.9j c.620j d.621.2j plz explain with solution

1
by sweetygannerla

2015-04-15T22:30:56+05:30

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Volume V = 67.2 litres  of Helium  at  STP

ΔT = 15⁰K
1 mole of an ideal gas occupies 22.4 litres at STP.
So number of moles of Helium gas  n = 67.2/22.4 = 3

we know that
γ = ratio of specific heats for an ideal mono atomic gas = 5/3
C_p = heat capacity at constant pressure for a mono atomic gas = 5/2 R
C_v = heat capacity at constant volume for a mono atomic gas = 3/2 R

Change in internal energy = n C_v ΔT
= 3 * 3/2 * 8.31 J/mol/°K  * 15°K
= 560.925 Joules

There is no change in the volume and hence no work done in heating the gas by 15 deg.

Heat supplied = change in internal energy
= 560.925 Joules