# Equal volumes of monoatomic and diatomic gas are given equal quantities of heat at the same temperature . which gas will have higher temperature ?

1
by namku

## Answers

The Brainliest Answer!
2015-04-25T00:36:45+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Volume of both gases = V  (initial and final), as we assume they are in fixed containers.
number of moles of each gas = n  (assume)
Initial temperature of both gases = T
Quantity of heat given to each gas = Q

Mono-atomic gas
Ratio of specific heats = γ₁ = 5/3
Molar Heat capacity at constant volume = = 3/2 R
Pressure  initial = P₁    ,    final = P₁',         Final temperature = T₁'

P₁ V = n R T ,       P₁'  V = n R T₁'      =>    P₁' / P₁ = T₁' / T

Diatomic gas
ratio of specific heats = γ₂ = 7/5
Molar Heat capacity at constant volume = = 5/2 R
pressure  initial  = P₂  ,    final pressure = P₂'  ,       final temperature = T₂'

P₂ V = n R T   ,       P₂'  V = n R T₂'        =>      P₂' / P₂ = T₂' / T

==>    P₂  =  P₁          and           P₂' / P₁'  =   T₂' / T₁'
=================

There is no change in volumes.  Hence the work done W by each gas is zero.

Q = ΔU + W
Q = ΔU = change in internal energy =

As molar heat capacity for the diatomic gas is more than that of monoatomic gas, the temperature increase for the diatomic gas will be less.   Thus, the mono-atomic gas will have higher temperature.

is there a shorter method ?
the last 6 lines after the ========== line are enough.
k ty