Two moles of an ideal gas at 300 K were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if R is the gas constant.

Question

Two moles of an ideal gas at 300 K were cooled at constant volume so that the pressure is reduced to half the initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature. Find the total heat absorbed by the gas, if R is the gas constant. (A) 150 R J (B) 300 R J (C) 75 R J (D) 100 R J

Tardigrade Admin · Accepted Answer

For 1 mol of gas, Q=Cv Δ T+P Δ T At constant volume, Δ T=0 For 2 moles of gas, Δ=2 Cv Δ T From P V=n R T=2 R × 300 and (P/2) V=2 RT f ∴ Tf=150 K ∴ Q=2 Cv(Tf-Ti)=2 Cv(150-300)=-300 Cv J In the next process, Q=2 Cp Δ T=2 Cp (300-150)=300 Cp J ∴ Net heat absorbed =-300 Cv+300 Cp =300(Cp-Cv)=300 R J

$150 R J$

$300 R J$

$75 R J$

$100 R J$

150RJ

300RJ

75RJ

100RJ

$150 R J$

$300 R J$

$75 R J$

$100 R J$