Question 688: Thermodynamics & KTG

Question

A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is $\left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]$

Accepted Answer

When a quantity of heat ' $ Q $ ' is supplied to a monoatomic ideal gas that expands at constant pressure, the fraction of heat converted into work can be determined using the specific heat ratios. Given that the adiabatic index $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$, we can reason as follows:
The relationship between the heat supplied ($\Delta Q$) and the change in internal energy ($\Delta U$) is given by the ratio of specific heats:
$    \frac{\Delta Q}{\Delta U} = \gamma = \frac{5}{3}    $
By rearranging to find the work done ($W$), we use:
$    \frac{\Delta Q - \Delta U}{\Delta Q} = \frac{5 - 3}{5}    $
Therefore, the fraction of heat converted into work is:
$    \frac{W}{\Delta Q} = \frac{2}{5}    $
This indicates that $\frac{2}{5}$ of the heat $Q$ is converted into work during the expansion process.

Answer

$3: 5$

Answer

$5: 3$

Answer

$2: 5$

Answer

$3: 2$

Thermodynamics & KTG

A quantity of heat ' Q ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is \left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]

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