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

Respuesta :

Answer:

Explanation:

Given

Volume of fixed chamber [tex]V=1 m^3[/tex]

Initial Temperature [tex]T_1=300 K[/tex]

Final Temperature [tex]T_2=400 K[/tex]

Heat Supplied [tex]Q=10 J[/tex]

From First law of thermodynamics

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

[tex]\Delta U=Q-W[/tex]

as the volume is fixed therefore work

[tex]W=\int PdV=0[/tex]

thus [tex]\Delta U=mc_v\Delta T=Q[/tex]

[tex]c_v[/tex] for mono-atomic gas is [tex]12.471 J/K-mol[/tex]

[tex]n\times 12.471\times (400-300)=10[/tex]

[tex]n=0.008018 mol[/tex]

and 1 mole contains [tex]6.022\times 10^{23} molecules[/tex]

thus  No of molecules[tex]=0.008018\times 6.022\times 10^{23}[/tex]

No of molecules[tex]=4.82\times 10^{21} molecules[/tex]

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