Two mole of an ideal gas is heated at constant pressure of one atmosphere from 27° C to 127° C. If C v , m =20+10-2 T JK -1 mol -1, then q and Δ U for the process are respectively:

Question

Two mole of an ideal gas is heated at constant pressure of one atmosphere from 27° C to 127° C. If C v , m =20+10-2 T JK -1 mol -1, then q and Δ U for the process are respectively: (A) 6362.8 J , 4700 J (B) 3037.2 J , 4700 J (C) 7062.8,5400 J (D) 3181.4 J, 2350 J

Tardigrade Admin · Accepted Answer

w =- nR Δ T =-2 × 8.314 × 100=-1662.8 J Δ U = n ∫ limits300400(20+10-2 T) d T =2[2 × 100+(10-2/2)(4002-3002)]=4700 J 4700= q -1662.8 ∴ q =6362.8 J

Q. Two mole of an ideal gas is heated at constant pressure of one atmosphere from $2 7^{\circ} C$ to $12 7^{\circ} C$ . If $C_{v, m} = 20 + 1 0^{- 2} T J K^{- 1} m o l^{- 1},$ then $q$ and $Δ U$ for the process are respectively:

6362.8 J , 4700 J

3037.2 J , 4700 J

7062.8,5400 J

3181.4 J, 2350 J

$w = - n R Δ T = - 2 \times 8.314 \times 100 = - 1662.8 J$

$Δ U = n$

$300 \int 400 (20 + 1 0^{- 2} T) d T$

$= 2 [2 \times 100 + \frac{1 0 ^{- 2}}{2} (40 0^{2} - 30 0^{2})] = 4700 J$

$4700 = q - 1662.8$

$∴ q = 6362.8 J$

Q. Two mole of an ideal gas is heated at constant pressure of one atmosphere from 27∘C to 127∘C. If Cv,m​=20+10−2TJK−1mol−1, then q and ΔU for the process are respectively: