Question

$10mol$ of an ideal gas is heated at constant pressure of $1$ atmosphere from $27^\circ C$ to $127^\circ C$ . If $C_{v , m}=\left(20 + \left(10\right)^{- 2} T\right)\left(JK\right)^{- 1}\left(mol\right)^{- 1}$ then $ΔH$ for the process is :-

• A. $23500J$
• B. $25500J$
• C. $31814J$
• D. $22000J$

Answer 1

Answer: (C)

$\displaystyle \int dH=n\displaystyle \int C_{p , m}dT$
$ΔH=10\displaystyle \int _{300 K}^{400 K}\left(C_{v , m} + R\right)dT$
$ΔH=10\displaystyle \int _{300 K}^{400 K}\left(20 + \left(10\right)^{- 2} T + 8 . 314\right)dT$
$ΔH=31814J$