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

Step-by-step 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* 12.471* (400-300)=10`

`n=0.008018 mol`

and 1 mole contains
`6.022* 10^(23) molecules`

thus No of molecules
`=0.008018* 6.022* 10^(23)`

No of molecules
`=4.82* 10^(21) molecules`