A monoatomic gas performs a work of (Q/4) where Q is the heat supplied to it. The molar heat capacity of the gas will be R during this transformation. Where R is the gas constant.

Question

A monoatomic gas performs a work of (Q/4) where Q is the heat supplied to it. The molar heat capacity of the gas will be R during this transformation. Where R is the gas constant. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Δ Q =Δ E + WD ⇒ Q =Δ E +( Q /4) ⇒ n (3 R /2) Δ T =Δ E =(3 Q /4) ∴ n Δ T =( Q /2 R ) ∴ C =2 R

Q. A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas will be _______ $R$ during this transformation.
Where $R$ is the gas constant.

$Δ Q = Δ E + W D \Rightarrow Q = Δ E + \frac{Q}{4}$
$\Rightarrow n \frac{3 R}{2} Δ T = Δ E = \frac{3 Q}{4}$
$∴ n Δ T = \frac{Q}{2 R}$
$∴ C = 2 R$

Q. A monoatomic gas performs a work of 4Q​ where Q is the heat supplied to it. The molar heat capacity of the gas will be _______R during this transformation. Where R is the gas constant.

ΔQ=ΔE+WD⇒Q=ΔE+4Q​ ⇒n23R​ΔT=ΔE=43Q​ ∴nΔT=2RQ​ ∴C=2R

Q. A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas will be _______ $R$ during this transformation.
Where $R$ is the gas constant.

$Δ Q = Δ E + W D \Rightarrow Q = Δ E + \frac{Q}{4}$
$\Rightarrow n \frac{3 R}{2} Δ T = Δ E = \frac{3 Q}{4}$
$∴ n Δ T = \frac{Q}{2 R}$
$∴ C = 2 R$