Question

An ideal gas is heated in a vessel at
constant pressure. The fraction of heat
used to do work by the gas
А. is more for diatomic gas than for
monoatomic gas
B. is more for monoatomic gas
than for diatomic gas
C. is equal for both
D. can be more, less or equal
depending on mass​

Answer 1

Answer:

A) is ur correct answer

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Answer 2

Heat Energy added = Change in Internal Energ + Work done

∴ ΔH = ΔU + W  ------(i)

For a constant pressure, i.e: isobaric process,

ΔH = n$C_{p}$ΔT

ΔU = n$C_{v}$ΔT

W = nRΔT

∴ Equation (i) becomes,

n$C_{p}$ΔT = n$C_{v}$ΔT + nRΔT

Fraction of heat used to do work by the gas =  $\frac{nR*dT}{nC_{p} *dT + nR*dT}$

∴ Fraction of heat used to do work by the gas = $\frac{R}{C_{p}+R }$ ---- (ii)

For monoatomic gas,

$C_{p}$ = $\frac{5R}{2}$

∴ Equation (ii) becomes,

Fraction of heat used to do work by the gas for monoatomic gas

= $\frac{2}{7}$

For diatomic gas,

$C_{p}$ = $\frac{7R}{2}$

∴ Equation (ii) becomes,

Fraction of heat used to do work by the gas for diatomic gas

= $\frac{2}{9}$

as $\frac{2}{7}$ > $\frac{2}{9}$,

Fraction of heat used to do work by the gas for monoatomic gas > Fraction of heat used to do work by the gas for diatomic gas.

∴ Option B