One mole of an ideal gas requires 207J heat to raise the temperature by 10K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10K, the heat required is:- (Given gas constant R=8.3Jmol- 1K )

Question

One mole of an ideal gas requires 207J heat to raise the temperature by 10K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10K, the heat required is:- (Given gas constant R=8.3Jmol- 1K ) (A) 198.7J (B) 29J (C) 215.3J (D) 124J

Tardigrade Admin · Accepted Answer

(Δ Q)P=μ CpΔ T⇒ 207=1× Cp× 10 ⇒ CP=20.7( text Joule /mol - K). Also CP-CV=R ⇒ CV=CP-R=20.7-8.3=12.4( text Joule /mole - K) So, (Δ Q)V=μ CVΔ T=1× 12.4× 10=124J

Q. One mole of an ideal gas requires $207 J$ heat to raise the temperature by $10 K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10 K,$ the heat required is:-
(Given gas constant $R = 8.3 J m o l^{- 1} K$ )

$198.7 J$

$29 J$

$215.3 J$

$124 J$

$(Δ Q)_{P} = μ C_{p} Δ T \Rightarrow 207 = 1 \times C_{p} \times 10$
$\Rightarrow C_{P} = 20.7 \frac{Joule}{m o l - K} .$ Also $C_{P} - C_{V} = R$
$\Rightarrow C_{V} = C_{P} - R = 20.7 - 8.3 = 12.4 \frac{Joule}{m o l e - K}$
So, $(Δ Q)_{V} = μ C_{V} Δ T = 1 \times 12.4 \times 10 = 124 J$

Q. One mole of an ideal gas requires 207J heat to raise the temperature by 10K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10K, the heat required is:- (Given gas constant R=8.3Jmol−1K )

198.7J

29J

215.3J

124J