Question

Six moles of $ O_2 $ gas is heated from $ 20^{\circ}C $ to $ 35^{\circ}C $ at constant volume. If specific heat capacity at constant pressure is $ 8\,cal/mol-K $ and $ R= 8.31 \,J/mol -K $ what is change in internal energy of gas

• A. $ 180\,cal $
• B. $ 300\,cal $
• C. $ 360\,cal $
• D. $ 540\,cal $

Answer 1

Answer: (D)

Consider $n$ moles of a gas which undergo isochoric process, i.e., $V=$ constant. From first law of thermodynamics,
$ΔQ = ΔW + ΔU \quad ...(i) $
Here, $ΔW = 0$ as $V =$ constant
$ΔQ = \,{}^{n}C_{V} ΔT $
Substituting in Eq.(i), we get
$ΔU = nC_V ΔT \quad ...(ii)$
Mayor’s relation can be written as
$C_P - C_V = R $
$⇒ C_V = C_P −R \quad ...(iii)$
From Eqs.(ii) and (iii), we have
$ΔU = n(C_P - R)ΔT $
Given, $n = 6, C_P = 8 \,cal / mol - K$,
$R = 8. 31\, J/mol - K$
$≈ 2 \,cal/mol - K$
Hence, $ΔU = 6(8 - 2)(35 - 20)$
$= 6 × 6 × 15 = 540\, cal$