When Q amount of heat is supplied to an ideal monoatomic gas, the gas performs (Q/2) amount of work on its surrounding, then the molar heat capacity for the process is

Question

When Q amount of heat is supplied to an ideal monoatomic gas, the gas performs (Q/2) amount of work on its surrounding, then the molar heat capacity for the process is (A) 2R (B) 1.5R (C) 3R (D) 2.5R

Tardigrade Admin · Accepted Answer

Q=Δ U+W Q=Δ U+(Q/2) ⇒ Δ U=(Q/2) ⇒ Δ U=(3/2)nRΔ T=(Q/2) C=(Q/n Δ T) ⇒ C=3R

Q. When $Q$ amount of heat is supplied to an ideal monoatomic gas, the gas performs $\frac{Q}{2}$ amount of work on its surrounding, then the molar heat capacity for the process is

$2 R$

$1.5 R$

$3 R$

$2.5 R$

$Q = Δ U + W$
$Q = Δ U + \frac{Q}{2}$
$\Rightarrow Δ U = \frac{Q}{2}$
$\Rightarrow$ $Δ U = \frac{3}{2} n R Δ T = \frac{Q}{2}$
$C = \frac{Q}{n Δ T}$
$\Rightarrow C = 3 R$

Q. When Q amount of heat is supplied to an ideal monoatomic gas, the gas performs 2Q​ amount of work on its surrounding, then the molar heat capacity for the process is

2R

1.5R

3R

2.5R