A monatomic ideal gas is heated while at a constant volume of 1.00 * 10^-3 m^3,...

A monatomic ideal gas is heated while at a constant volume of 1.00 * 10^-3 m^3, using a 10 watt heater. The pressure of the gas increases by 5.0 * 10^4 Pa. How long was the heater on?

Expert Solution

At constant volume work =0

so heat change = change in internal energy = n Cv(T2-T1)

heat change = power*time =10*t

10*t=n Cv(T2-T1) =3Rn(T2-T1)/2 Cv =3R/2 for monoatomic

use ideal gas equation

P1V1=nRT1 P2V1=nRT2

substact above equations

T2 - T1= V1(P2-P1)/nR

so 10*t = 1.5 nR*V1(P2-P1)/nR =1.5*V1(P2-P1)

10*t= V1(P2-P1) =1.5* 10^(-3) * 5*10^(4 ) [P2-P1 =5*10^4 pas given ]

so t= 7.5 sec

genius_generous answered 3 weeks ago

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