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Internal Energy

One mole of a...

Question

One mole of an ideal monoatomic gas is initially at $300 K$ . Find the final temperature (in $K$ ) if $200 J$ of heat are added at constant volume.

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Solution

Heat supplied to a system is given by:

$Δ q = \int n C d T$ Where n is the number of moles of the gas and C is the specific heat capacity for the process.

Here it is given that the process is a constant volume process.
$C = C_{v}$

i.e. $Δ T = \frac{q}{n C_{v}}$

For a monoatomic ideal gas. $C_{v} = \frac{R}{γ - 1} γ = \frac{5}{3}$
$C_{v} = \frac{3}{2} R$

$Δ T = \frac{2 q}{3 n R} = \frac{2 \times 200}{3 \times 1 \times 8.314} = 16 K$

i.e. $Δ T = T_{2} - T_{1} = 16 K$

$T_{2} = T_{1} + 16 = 316 K$

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