Question

a chamber with a fixed volume of 1.0 meters cubed contains a monatomic gas at 3.00 *10^K. The chamber is heated to a temperature of 400 K. This operation requires 10.0 J of heat. How many gas molecules are in the chamber

Answer 1

Answer:

Explanation:

Given

Volume of fixed chamber $V=1 m^3$

Initial Temperature $T_1=300 K$

Final Temperature $T_2=400 K$

Heat Supplied $Q=10 J$

From First law of thermodynamics

Change in internal energy of the system is equal to heat added minus work done by the system

$\Delta U=Q-W$

as the volume is fixed therefore work

$W=\int PdV=0$

thus $\Delta U=mc_v\Delta T=Q$

$c_v$ for mono-atomic gas is $12.471 J/K-mol$

$n\times 12.471\times (400-300)=10$

$n=0.008018 mol$

and 1 mole contains $6.022\times 10^{23} molecules$

thus  No of molecules$=0.008018\times 6.022\times 10^{23}$

No of molecules$=4.82\times 10^{21} molecules$