A certain amount of an ideal monatomic gas needs 20 J of heat energy to raise its temperature by 10° C at constant pressure. The heat needed for the same temperature rise at constant volume will be

Question

A certain amount of an ideal monatomic gas needs 20 J of heat energy to raise its temperature by 10° C at constant pressure. The heat needed for the same temperature rise at constant volume will be (A) 30 J (B) 12 J (C) 200 J (D) 215.3 J

Tardigrade Admin · Accepted Answer

Δ Q=n CP Δ T 20=n CP × 10 ...(1) Δ U=n CV Δ T Δ U=n (CP/&gamma;) Δ T ∵ &gamma; text mono =5 / 3 Δ U=12 J

Q. A certain amount of an ideal monatomic gas needs $20 J$ of heat energy to raise its temperature by $1 0^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be

30 J

12 J

200 J

215.3 J

$Δ Q = n C_{P} Δ T$
$20 = n C_{P} \times 10 ... (1)$
$Δ U = n C_{V} Δ T$
$Δ U = n \frac{C _{P}}{γ} Δ T$
${∵ γ_{mono} = 5/3}$
$Δ U = 12 J$

Q. A certain amount of an ideal monatomic gas needs 20J of heat energy to raise its temperature by 10∘C at constant pressure. The heat needed for the same temperature rise at constant volume will be