A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas ((W/Q)) is

Question

A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas ((W/Q)) is (A) (2/5) (B) (3/5) (C) (2/3) (D) 1

Tardigrade Admin · Accepted Answer

Take 1 mole of gas Cp Δ T=Cv Δ T+Δ W ∴ Δ W=(Cp-Cv) Δ T Fraction of heat converted into work (Δ W/Δ Q)=((Cp-Cv) Δ T/Cp Δ T) =-1-(1/&gamma;) =(1-(3/5))=(2/5)

Q. A quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas $(\frac{W}{Q})$ is

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{2}{3}$

1

Take 1 mole of gas $C_{p} Δ T = C_{v} Δ T + Δ W$
$∴ Δ W = (C_{p} - C_{v}) Δ T$
Fraction of heat converted into work
$\frac{Δ W}{Δ Q} = \frac{( C _{p} - C _{v} ) Δ T}{C _{p} Δ T}$
$= - 1 - \frac{1}{γ} = (1 - \frac{3}{5}) = \frac{2}{5}$

Q. A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas (QW​) is

52​

53​

32​

1

Take 1 mole of gas Cp​ΔT=Cv​ΔT+ΔW ∴ΔW=(Cp​−Cv​)ΔT Fraction of heat converted into work ΔQΔW​=Cp​ΔT(Cp​−Cv​)ΔT​ =−1−γ1​=(1−53​)=52​

Q. A quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas $(\frac{W}{Q})$ is

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{2}{3}$

Take 1 mole of gas $C_{p} Δ T = C_{v} Δ T + Δ W$
$∴ Δ W = (C_{p} - C_{v}) Δ T$
Fraction of heat converted into work
$\frac{Δ W}{Δ Q} = \frac{( C _{p} - C _{v} ) Δ T}{C _{p} Δ T}$
$= - 1 - \frac{1}{γ} = (1 - \frac{3}{5}) = \frac{2}{5}$