10mol of an ideal gas is heated at constant pressure of 1 atmosphere from 27° C to 127° C . If Cv , m=(20 + (10)- 2 T)(JK)- 1(mol)- 1 then ΔH for the process is :-

Question

10mol of an ideal gas is heated at constant pressure of 1 atmosphere from 27° C to 127° C . If Cv , m=(20 + (10)- 2 T)(JK)- 1(mol)- 1 then ΔH for the process is :- (A) 23500J (B) 25500J (C) 31814J (D) 22000J

Tardigrade Admin · Accepted Answer

displaystyle ∫ dH=n displaystyle ∫ Cp , mdT ΔH=10 displaystyle ∫ 300 K400 K(Cv , m + R)dT ΔH=10 displaystyle ∫ 300 K400 K(20 + (10)- 2 T + 8 . 314)dT ΔH=31814J

Q. $10 m o l$ of an ideal gas is heated at constant pressure of $1$ atmosphere from $2 7^{\circ} C$ to $12 7^{\circ} C$ . If $C_{v, m} = (20 + (10)^{- 2} T) (J K)^{- 1} (m o l)^{- 1}$ then $Δ H$ for the process is :-

$23500 J$

$25500 J$

$31814 J$

$22000 J$

$\int d H = n \int C_{p, m} d T$
$Δ H = 10 \int_{300 K}^{400 K} (C_{v, m} + R) d T$
$Δ H = 10 \int_{300 K}^{400 K} (20 + (10)^{- 2} T + 8.314) d T$
$Δ H = 31814 J$

Q. 10mol of an ideal gas is heated at constant pressure of 1 atmosphere from 27∘C to 127∘C . If Cv,m​=(20+(10)−2T)(JK)−1(mol)−1 then ΔH for the process is :-

23500J

25500J

31814J

22000J