Question 621: Thermodynamics & KTG

Question

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas
at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close
to _______.

Accepted Answer

As work done on gas and heat supplied to the gas are zero,
$$ 	herefore $$ Total internal energy of gases remain same.
u
1
+ u
2
= u
1
' + u
2
'
We know, $$\Delta $$U = nC
v
$$\Delta $$T
$$ 	herefore $$ $$\left( {0.1 	imes {{3R} \over 2} 	imes 200} ight) + \left( {0.05 	imes {{3R} \over 2} 	imes 400} ight)$$ = $$\left( {0.15 	imes {{3R} \over 2} 	imes {T_f}} ight)$$
$$ \Rightarrow $$ (20 + 20) = 0.15 T
f
$$ \Rightarrow $$ T
f
= 266.67

Thermodynamics & KTG

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.

Choose the correct answer: